First: try to give more power to your motherboard.
BPPC are power-hungry.
So you must connect a floppy power connector from your power supply to the floppy power connector on your motherboard.
Generally BPPC become more stable.
Second:
check also your motherboard revision...
I know many BPPCs have serious problem with some rev. 1D4: for example my rev 1D4 doesn't start with my BPPC, getting a black screen like you.
So try your card with another motherboard.
If it doesn't start even giving more power or with other mobo revisions, then it's dead and you can try to repair it.
JJB at AmigaCenter is great for repairing BPPC cards.