If a compressor goes out, it tends to be pretty obvious. Something might seize, there might be smoke, there might be a loud squealing sound, etc. IIRC, the TrailBlazer uses a cycling clutch compressor, so it should cycle off when the pressure reaches a certain point, and cycle back on when it gets reduced to a certain point. If it fails to do that, try disconnecting the low pressure switch and jumping the wires. If that doesn't engage it, then you probably have a bad low pressure switch. If that doesn't solve the problem, try hooking a manifold gauge set to the AC system... if your pressure readings are particularly low, especially on the high pressure side of the system, then a defective compressor is a possibility, although there are other possible causes, as well. Narrowing it down requires a pretty comprehensive knowledge of AC systems, and you're probably better off to let a qualified automotive technician handle this.
Yes a bad cold control will not let the compresser come on to check bypass cold control if compresser comes on replace cold control.
we found a bad relay.
It could be a bad bearing in the idler pully, A/C clutch, ect. Try turning on the A/C to see if it changes the squeek.
your switch that controls the compresser might be bad.
I think this has an electric fan clutch. If it does then check to make sure it is bolted on good and if that isn't the case then a wobble would indicate a bad fan clutch.
over heat
If the car will not start...the spark-plug is bad.
Bad plug or something is misassembled.
Try to start it
yes it can go bad! check fuses and wiring first! usually its the ac clutch that does not work!! if low or out of coolant clutch will not recycle.
Fuel pressure test.
If your hear "ticking" and have to use WD40