So far this is not rocket science. How the heck did you determine the the 134a charge was ok with the compressor not engaged? The only way to know that is to recover all refrigerant and weigh it! Pressures are approximations that are highly temperature dependant and mean almost nothing if system doesn't engage.
Ex: A pressure with system off either high or low side will read about the pressure in psi as the ambient temp in degrees F. Anything less you are near out of refrigerant! It's leaking!
If you want to see compressor come on just jumper wire the low side switch on your accumulator (I think it's there) if a two wire switch compressor will probably click on. You test for 12V there going in and at about 30psi pressure it makes it's own connection and disconnects when too low which guards against hydraulic lock at the compressor.
If no power to the switch you check out fuses and relays.
What year is this S-10 Blazer? If 93 or newer it has a high side switch to cut out compressor if too high but that's in the 300s psi. Don't mess with that switch. If you don't which is which don't mess with them at all.
Come visit the folks at
www.autoACsystems.com/tomgreenleaf -- click on the CoolZone for A/C help,
T
Tom Greenleaf - MetroWest Boston - USA
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http://www.autoacsystems.com/tomgreenleaf/