Yet another SD card initialization error (Leonardo)

The SD card reader embedded into a 3.5" TFT LCD simply will not work with the Leonardo. I've intercepted all the pins except for the CS pin and rerouted them to the ICSP header already. I double and triple-checked the pins and they're all intact and in the right spots. I'm using pin 10 for the CS pin. Every SD library has failed, including SdFat, built-in SD library, and Adafruit SD. I've tried setting the ICSP header SS pin and pin 10 to OUTPUT and HIGH and every combination of that but none of it works. The SD shield simply can't initialize. It took hours of searching for a solution earlier and I only got it to work with the SDInfo example 1 time. The shield isn't broken as far as I can tell, so what's wrong? It seems i've done everything every forum post has suggested. SdFat gives a 0x20 error indicating that sending commands to the thing doesn't work at all. The LCD part works fine on the shield.

This is using SdInfo example btw, and just in case here's the code of that:

/*
 * This program attempts to initialize an SD card and analyze its structure.
 */
#include <SPI.h>
#include "SdFat.h"

// Set USE_SDIO to zero for SPI card access. 
#define USE_SDIO 0
/*
 * SD chip select pin.  Common values are:
 *
 * Arduino Ethernet shield, pin 4.
 * SparkFun SD shield, pin 8.
 * Adafruit SD shields and modules, pin 10.
 * Default SD chip select is the SPI SS pin.
 */
const uint8_t SD_CHIP_SELECT = 10;
/*
 * Set DISABLE_CHIP_SELECT to disable a second SPI device.
 * For example, with the Ethernet shield, set DISABLE_CHIP_SELECT
 * to 10 to disable the Ethernet controller.
 */
const int8_t DISABLE_CHIP_SELECT = 10;

#if USE_SDIO
// Use faster SdioCardEX
SdFatSdioEX sd;
// SdFatSdio sd;
#else // USE_SDIO
SdFat sd;
#endif  // USE_SDIO

// serial output steam
ArduinoOutStream cout(Serial);

// global for card size
uint32_t cardSize;

// global for card erase size
uint32_t eraseSize;
//------------------------------------------------------------------------------
// store error strings in flash
#define sdErrorMsg(msg) sd.errorPrint(F(msg));
//------------------------------------------------------------------------------
uint8_t cidDmp() {
  cid_t cid;
  if (!sd.card()->readCID(&cid)) {
    sdErrorMsg("readCID failed");
    return false;
  }
  cout << F("\nManufacturer ID: ");
  cout << hex << int(cid.mid) << dec << endl;
  cout << F("OEM ID: ") << cid.oid[0] << cid.oid[1] << endl;
  cout << F("Product: ");
  for (uint8_t i = 0; i < 5; i++) {
    cout << cid.pnm[i];
  }
  cout << F("\nVersion: ");
  cout << int(cid.prv_n) << '.' << int(cid.prv_m) << endl;
  cout << F("Serial number: ") << hex << cid.psn << dec << endl;
  cout << F("Manufacturing date: ");
  cout << int(cid.mdt_month) << '/';
  cout << (2000 + cid.mdt_year_low + 10 * cid.mdt_year_high) << endl;
  cout << endl;
  return true;
}
//------------------------------------------------------------------------------
uint8_t csdDmp() {
  csd_t csd;
  uint8_t eraseSingleBlock;
  if (!sd.card()->readCSD(&csd)) {
    sdErrorMsg("readCSD failed");
    return false;
  }
  if (csd.v1.csd_ver == 0) {
    eraseSingleBlock = csd.v1.erase_blk_en;
    eraseSize = (csd.v1.sector_size_high << 1) | csd.v1.sector_size_low;
  } else if (csd.v2.csd_ver == 1) {
    eraseSingleBlock = csd.v2.erase_blk_en;
    eraseSize = (csd.v2.sector_size_high << 1) | csd.v2.sector_size_low;
  } else {
    cout << F("csd version error\n");
    return false;
  }
  eraseSize++;
  cout << F("cardSize: ") << 0.000512*cardSize;
  cout << F(" MB (MB = 1,000,000 bytes)\n");

  cout << F("flashEraseSize: ") << int(eraseSize) << F(" blocks\n");
  cout << F("eraseSingleBlock: ");
  if (eraseSingleBlock) {
    cout << F("true\n");
  } else {
    cout << F("false\n");
  }
  return true;
}
//------------------------------------------------------------------------------
// print partition table
uint8_t partDmp() {
  mbr_t mbr;
  if (!sd.card()->readBlock(0, (uint8_t*)&mbr)) {
    sdErrorMsg("read MBR failed");
    return false;
  }
  for (uint8_t ip = 1; ip < 5; ip++) {
    part_t *pt = &mbr.part[ip - 1];
    if ((pt->boot & 0X7F) != 0 || pt->firstSector > cardSize) {
      cout << F("\nNo MBR. Assuming Super Floppy format.\n");
      return true;
    }
  }
  cout << F("\nSD Partition Table\n");
  cout << F("part,boot,type,start,length\n");
  for (uint8_t ip = 1; ip < 5; ip++) {
    part_t *pt = &mbr.part[ip - 1];
    cout << int(ip) << ',' << hex << int(pt->boot) << ',' << int(pt->type);
    cout << dec << ',' << pt->firstSector <<',' << pt->totalSectors << endl;
  }
  return true;
}
//------------------------------------------------------------------------------
void volDmp() {
  cout << F("\nVolume is FAT") << int(sd.vol()->fatType()) << endl;
  cout << F("blocksPerCluster: ") << int(sd.vol()->blocksPerCluster()) << endl;
  cout << F("clusterCount: ") << sd.vol()->clusterCount() << endl;
  cout << F("freeClusters: ");
  uint32_t volFree = sd.vol()->freeClusterCount();
  cout <<  volFree << endl;
  float fs = 0.000512*volFree*sd.vol()->blocksPerCluster();
  cout << F("freeSpace: ") << fs << F(" MB (MB = 1,000,000 bytes)\n");
  cout << F("fatStartBlock: ") << sd.vol()->fatStartBlock() << endl;
  cout << F("fatCount: ") << int(sd.vol()->fatCount()) << endl;
  cout << F("blocksPerFat: ") << sd.vol()->blocksPerFat() << endl;
  cout << F("rootDirStart: ") << sd.vol()->rootDirStart() << endl;
  cout << F("dataStartBlock: ") << sd.vol()->dataStartBlock() << endl;
  if (sd.vol()->dataStartBlock() % eraseSize) {
    cout << F("Data area is not aligned on flash erase boundaries!\n");
    cout << F("Download and use formatter from www.sdcard.org!\n");
  }
}
//------------------------------------------------------------------------------
void setup() {
  Serial.begin(9600);
  
  // Wait for USB Serial 
  while (!Serial) {
    SysCall::yield();
  }

  // use uppercase in hex and use 0X base prefix
  cout << uppercase << showbase << endl;

  // F stores strings in flash to save RAM
  cout << F("SdFat version: ") << SD_FAT_VERSION << endl;
#if !USE_SDIO  
  if (DISABLE_CHIP_SELECT < 0) {
    cout << F(
           "\nAssuming the SD is the only SPI device.\n"
           "Edit DISABLE_CHIP_SELECT to disable another device.\n");
  } else {
    cout << F("\nDisabling SPI device on pin ");
    cout << int(DISABLE_CHIP_SELECT) << endl;
    pinMode(DISABLE_CHIP_SELECT, OUTPUT);
    digitalWrite(DISABLE_CHIP_SELECT, HIGH);
  }
  cout << F("\nAssuming the SD chip select pin is: ") <<int(SD_CHIP_SELECT);
  cout << F("\nEdit SD_CHIP_SELECT to change the SD chip select pin.\n");
#endif  // !USE_SDIO  
}
//------------------------------------------------------------------------------
void loop() {
  // Read any existing Serial data.
  do {
    delay(10);
  } while (Serial.available() && Serial.read() >= 0);

  // F stores strings in flash to save RAM
  cout << F("\ntype any character to start\n");
  while (!Serial.available()) {
    SysCall::yield();
  }

  uint32_t t = millis();
#if USE_SDIO
  if (!sd.cardBegin()) {
    sdErrorMsg("\ncardBegin failed");
    return;
  }
#else  // USE_SDIO
  // Initialize at the highest speed supported by the board that is
  // not over 50 MHz. Try a lower speed if SPI errors occur.
  if (!sd.cardBegin(SD_CHIP_SELECT, SD_SCK_MHZ(50))) {
    sdErrorMsg("cardBegin failed");
    return;
  }
 #endif  // USE_SDIO 
  t = millis() - t;

  cardSize = sd.card()->cardSize();
  if (cardSize == 0) {
    sdErrorMsg("cardSize failed");
    return;
  }
  cout << F("\ninit time: ") << t << " ms" << endl;
  cout << F("\nCard type: ");
  switch (sd.card()->type()) {
  case SD_CARD_TYPE_SD1:
    cout << F("SD1\n");
    break;

  case SD_CARD_TYPE_SD2:
    cout << F("SD2\n");
    break;

  case SD_CARD_TYPE_SDHC:
    if (cardSize < 70000000) {
      cout << F("SDHC\n");
    } else {
      cout << F("SDXC\n");
    }
    break;

  default:
    cout << F("Unknown\n");
  }
  if (!cidDmp()) {
    return;
  }
  if (!csdDmp()) {
    return;
  }
  uint32_t ocr;
  if (!sd.card()->readOCR(&ocr)) {
    sdErrorMsg("\nreadOCR failed");
    return;
  }
  cout << F("OCR: ") << hex << ocr << dec << endl;
  if (!partDmp()) {
    return;
  }
  if (!sd.fsBegin()) {
    sdErrorMsg("\nFile System initialization failed.\n");
    return;
  }
  volDmp();
}

There are many 3.5" TFT with embedded SD card slot, which do you have?

Most of the boards I've seen have a regulator for 3.3V, but no level shifters for the SD, is your board different?

A SD card will not work with 5V signals and may even die from trying to.

I'm using this one. https://www.amazon.com/gp/product/B00UAA2XIC/ref=oh_aui_detailpage_o03_s00?ie=UTF8&psc=1.

It has both 3V and 5V pins so I'd assume it uses the right one.

After a look at the shield information I think the SD should work on a Leonardo if you rerouted the SPI pins correctly.

  // Initialize at the highest speed supported by the board that is
  // not over 50 MHz. Try a lower speed if SPI errors occur.
  if (!sd.cardBegin(SD_CHIP_SELECT, SD_SCK_MHZ(50))) {

Did you try lower speeds as advised?