First, check the usual stuff... fuses ok? central locking relay okay? .. if all is fine, then you will have to take out your drivers seat and pull up the carpet.
underneath here is where a bunch of wires ground to the chassis of the car... in time, this area gets rusted from moisture getting in the car and the ground gets killed. You'll have to fix this ground.
I know someone that spent over $1500 on their e36 trying to fix this problem from various shops and bmw dealerships. Took me two days of looking at wiring diagrams and testing/tracing every wire before I figured this out.
In your case, it seems like the trunk cylinder lock may be shorting somewhere or is not grounded. If you can get your hands on the wiring diagram for a Ti it would help a lot. You'll need to start testing wires and seeing which pulses are being sent and where the break is. I would check the grounds under the drivers seat first though.