SD writer code ultra light

You need to change this line:

  if (!card.init() ||

to:

  if (!card.init(speed, chipSelectPin ) ||

Where

uint8_t SdCard::init ( uint8_t speed,
uint8_t chipSelectPin
)

Initialize a SD flash memory card.

Parameters:
[in] speed Set SPI Frequency to F_CPU/2 if speed = 0 or F_CPU/4 if speed = 1.
[in] chipSelectPin SD chip select pin number.

Returns:
The value one, true, is returned for success and the value zero, false, is returned for failure.

In your case chipSelectPin is 4 and first try speed = 0.

You don't need this but it won't hurt:

  pinMode(10, OUTPUT);