SD card became unrecognized by card readers

I didn't understand why you linked a different sd card reader from ebay , my sd card reader is:

http://www.ebay.com/itm/SD-Card-Shield-Module-Memory-Read-Write-reader-Arduino-/150718852629?pt=UK_BOI_Electrical_Test_Measurement_Equipment_ET&hash=item23178b2e15#ht_2930wt_1270

I connected the card reader to my arduino nano like this:

5V pin to 5V pin
GND to GND
MOSI to pin 11
SS to pin 4
SCK to pin 13
MISO to pin 12

the output of the programs you ask for: (I remind you that the SD card is probably dead)

CardInfo example from SD.h using Arduino 1.0 output:
"
Initializing SD card...initialization failed. Things to check:

  • is a card is inserted?
  • Is your wiring correct?
  • did you change the chipSelect pin to match your shield or module?
    "

QuickStart example output:
"
SD chip select is the key hardware option.
Common values are:
Arduino Ethernet shield, pin 4
Sparkfun SD shield, pin 8
Adafruit SD shields and modules, pin 10
The default chip select pin number is pin 10

Enter the chip select pin number: 4

SD initialization failed.
Do not reformat the card!
Is the card correctly inserted?
Is chipSelect set to the correct value?
Is there a wiring/soldering problem?
errorCode: 0xa, errorData: 0x1

Restarting

Enter the chip select pin number:
"

SdInfo example output
"
SD chip select is the key hardware option.
Common values are:
Arduino Ethernet shield, pin 4
Sparkfun SD shield, pin 8
Adafruit SD shields and modules, pin 10
The default chip select pin number is pin 10

Enter the chip select pin number: 4

SD initialization failed.
Do not reformat the card!
Is the card correctly inserted?
Is chipSelect set to the correct value?
Is there a wiring/soldering problem?
errorCode: 0xa, errorData: 0x1

Restarting

Enter the chip select pin number:
"

all the checks made with the same config and with arduino 1.0
I used the ruined card