the bandgap voltage can be measured at the caps for Pin 11 (the bandgap pin)
With the sys_clock pin outputting 6.78MHz - i would think that the BG voltage you will measure will be correct.
When you read register 0x09, what value are you getting? if you are using 13.56MHz crystal, make sure that B7 is set to 0.
When you read register 0x00, what value are you getting? (should be 0x01 by default, if you are running the part from +5VDC, then you should be writing 0x21 into that register)
Then, for Type A support, first you should be writing a 0x88 into register 0x01, then sending the broken byte command (REQA or WupA, 0x26 or 0x52) to get the ATQA back...before you enter the anti-collision loop which will end with getting the card into a selected state, which will allow you to read data from the card.
so - most likely you are needing to answer the basic stuff above and share your layout, schematic and code flow before anyone can help much more. if you can cooperate in that manner, you can make it work here.