I am thinking it may be due to having 2 SPI devices wired together? (pins 13 and 11 are shared for connecting the LCD and SD card pins). I tried it with 3.3v and no change. Any help would be appreciated.
Could the fact that I'm using the ICSP pins for MISO, MOSI and SCK cause a problem? The LCD works fine using them.
Also, I've tried the SD card in another micro SD module wired up to my Uno, and it was read successfully.
When I get around to it I'll try hooking up only the SD pins, and leaving the LCD pins to see if that does anything.
Update :
Tried again with just the SD pins and no result. Checked the soldering on the module too, and as far as I can tell (without the looking at the datasheet) the SD seems connected. Looked at the datasheet and it wasn't much use.
I might just use a separate SD module, but that isn't ideal. If I ever buy another one of these I'll see if the SD part of this LCD/SD module is defective.