I've looked over the schematics and here are a few things to check:
In the under hood fuse panel check the Engine and the Main 60a fuses and
check that they have 12v on the fuses. Check the BCM/Engine Control 15a fuse and
the Engine Sensor 15a fuse.
Check the mini relays, replace them one by one with a known good one.
If you grounded the battery in the trunk to the frame, make sure you have
a ground from the frame to the engine.
You say the fob blinks the parking lights, clicks, cuts of the alarm, but doesn't unlock the door.
Does the security LED go off when it clicks to try to unlock the door? It should.
2005 GTO Fast - 2004 Z06 Faster - 1984 Honda V65 Magna Fastest