[jsbihn]

Cashville
There is actually a connector (i think only one) that if not completing the circuit correctly it will cause the key solenoid to not unlock.
The bad thing about this is you will have to undo the certer console, and possibly the center dash to get to this.

(been a while since I have been in there, so excuse me if my info is a little faulty)

The connector is actually on the drivers side of the shifter
If i remember correctly it is just a two wire connector, but you will need to look to see if it is shorting or if it is broken and not making the right connection.

I would bet the connector part is the culprit since it does get hot in the shifter area and it could be crispy and cooked.
I wouldnt go out and spend all the money on a new connector.
The nice thing is these are GM products and though you can spend the money, alot of times the fixes are easy and cheap if you think about it

I fixed my shifter slipping off the link with a 35 cents clip (instead of spending 125 dollars on a new cable setup I didnt need) and if that 35 cent fix fails, I already have a back up that cost me a whole 12 bucks in new parts and will NEVER fail. Just takes a little thinking
(now my M3...... different story)