Well if it isn't the CPU socket, then it is probably the cable.  Replace 
the TWGS CPU jumper cable.  You can make one with parts from Digikey. 
Parts are called DIP connector and Socket connector on pages 19 and 16 
respectively, part# C8PPG-4006M-ND and ASC40G-ND respectively.

Get one 40 pin 60mm Dip to Dip connector and cut it in half.  Get two 40 
pin Socket connecotrs and maybe two extra just because.  (I actully get 
mine from old IDE cables.)  Assemble slowly by squeezing evenly across 
the whole socket connector.  (Think vice.)  Then ohm out the cable to 
make sure it wired the same as the original cable.  If every other wire 
is incorrect, you need to open the socket connector and rotate each pin 
180 degrees and reassemble.

Thankx,
Ed

ToasterKing wrote:
> I have replaced the whole CPU socket on the GS motherboard.  That
> should take care of any bad solder joints AND any sprung contacts in
> the socket.  I checked solder joints on other sockets as well.  But
> that didn't work; I still get the same results.