Check to see if the IFAS board is behaving properly. You should see the RUS and CAS go high when receiving, and they'll go low when the receiver is squelched. The IFAS is the one with the big audio transformer and the metal can that says (DO NOT ADJUST...).
The pins on the IFAS will give you a wealth of info about what's going on in the receiver. Your unsquelched, low level audio will come out of the discriminator on the VSQ HI line. From there it will go through the pot wipers of the volume knob and the squelch knob. If you follow the squelch back on the SQ ARM pin, it will go into one of the black box ICs. That's where it analyzes the audio and determines whether to squelch or not. If you have no audio going back, it won't squelch (because it thinks it's currently receiving a high SINAD, genuine signal). You can get the most info check in the DC voltage levels out of U603, particularly pin 6 (CAS, which is independent of the received CG tone) and pin 8 (RUS, which goes high when receiver is unsquelched AND receiving the correct CG tone).
Check out this GE LBI for info on the IFAS board. The "Circuit Analysis" section does a very good job of explaining how each section works (including the squelch circuit)http://www.repeater-builder.com/ge/lbi-library/lbi-4986e.pdf
The very first thing I'd do is get out your oscilloscope and check these pins...
1. Noise or audio on VSQ HI
2. Noise or audio on SQ ARM pin (amplitude will go up and down as you play with the squelch knob)
3. Noise or audio on pin 2 of U603 IC
Then get our your handy-dandy VOM and check these...
4. 10V on the 10V pin
5. DC voltages around 0 on RUS and CAS (signals used by the repeater interface) when it should be squelched
6. DC voltage on RX Mute (which feeds the audio amp, and other things) around 0 when it should be squelched