The trunk release on my 97 deville will not operate from the dash button or the remote.BUT if I open the trunk with the key both the dash button and remote work for a limited time.This tells me both buttons and the solenoid are ok. I've checked the valet button it's ok.What could be the problem?

 

I have the same issue with my 96 Deville. I believe it may be the BCM having moments.
Sometimes I can pop the trunk fine, sometimes it will not pop no matter waht, and sometimes it double pops. I noticed one time I had the valet button engaged but the trunk still popped. dealer wants lots of money to repair though so
I just go with it