Error initiating microSD card in SPI mode
Looks on the surface like an electrical problem


Try a slower speed to start - you may have excessive capacitance in
your lines or a slow speed sdCard.
Are you polling until the card comes ready (see below)
Can you put a scope on it to check timings, these are critical?
Try a different SD card, or same card in a working device 
Can you transmit and receive to a different port on same device?
Can you transmit and receive to a different board using same PIC device?
Are you using microchip drivers / software libraries?
Have you got MISO/MOSI correctly wired?
Are the power requirements met - decoupling caps etc? 10uF+//100nF (some people use 100uF!!)
Are your output and input pins configured correctly?


At a later stage you may need to check the following - no particular order.


Check the 'endianness' of your SPI
Check your CRC
Double check your protocol


https://www.sdcard.org/downloads/pls/simplified_specs/archive/part1_110.pdf

pg 47 says that you need to poll the device until the card comes ready Are you doing this?