I've just done that measurement across the voltage regulator. I'm getting 0v between GND and VOut, and 0.15v (approx) between GND and VIn. This is powered from the Arduino via USB.
I think we've found the source of the problem. I've got a couple of spare modules, so I'll do the same test on those and see how it goes.
UPDATE:
I've just tried with another SD card module. I tested the voltage regulator chip on it, and that was good. However, upon testing it, I got the following results:
SdFat version: 10100
Assuming the SD is the only SPI device.
Edit DISABLE_CHIP_SELECT to disable another device.
Assuming the SD chip select pin is: 53
Edit SD_CHIP_SELECT to change the SD chip select pin.
type any character to start
init time: 125 ms
Card type: SDHC
Manufacturer ID: 0X3
OEM ID: SD
Product: SL16G
Version: 8.0
Serial number: 0XE4951B5D
Manufacturing date: 8/2011
cardSize: 15931.54 MB (MB = 1,000,000 bytes)
flashEraseSize: 128 blocks
eraseSingleBlock: true
OCR: 0XC0FF8000
SD Partition Table
part,boot,type,start,length
1,0X0,0XC,8192,31108096
2,0X0,0X0,0,0
3,0X0,0X0,0,0
4,0X0,0X0,0,0
error:
File System initialization failed.
SD errorCode: 0X30,0XFF
type any character to start
error: cardBegin failed
SD errorCode: 0X43,0X1
type any character to start
error: cardBegin failed
SD errorCode: 0X25,0XFF
type any character to start
error: cardBegin failed
SD errorCode: 0X25,0XFF
type any character to start
SdFat version: 10100
Assuming the SD is the only SPI device.
Edit DISABLE_CHIP_SELECT to disable another device.
Assuming the SD chip select pin is: 53
Edit SD_CHIP_SELECT to change the SD chip select pin.
type any character to start
error: cardBegin failed
SD errorCode: 0X25,0XFF
type any character to start
error: cardBegin failed
SD errorCode: 0X25,0XFF
type any character to start
error: cardBegin failed
SD errorCode: 0X25,0XFF
type any character to start
error: cardBegin failed
SD errorCode: 0X25,0XFF
type any character to start
error: cardBegin failed
SD errorCode: 0X25,0XFF
Aside from the first few error messages, it's exactly the same as before. I'm going to try it with the logic level converters in place.
I did check the voltage output from the regulator chip afterwards, and it was giving me 3.3 and 5 where expected.