2002 Chevrolet S-10 Compressor not ingaging

It will if it's nearly empty but there are many things that can prevent a compressor from coming on. You would have to know something about electrical circuits and follow a wiring diagram to troubleshoot the problem.

I checked and replaced the fuse in pass. compartment fuse block, same done to under hood fuse block. Also replaced relay in under hood fuse block. Is there anyway to check power to connection on compressor other than test light?

Sure a multimeter that costs a lot more than a test light.

What if I put a freon charge in first?

I do have a multimeter I can use.

You shouldn't be doing anything unless you have looked at the low and high pressure with a gauge and i don't mean one of those toy with read and green shaded areas that comes with the DIY death kits.

I take it this is a problem you think I need to have a qualified garage take care of.
They will charge the system and tell me it didn't work (Charge for freon & labor) then tell me I need a new compressor( Charge for compressor & labor again AND more freon. I think I will just buy another reman. compressor on line first, replace it at home then take it to a garage and have them charge it. MORE MONEY!! MORE MONEY!!

Thanks for the HELP!!

You are going to quadruple the cost of this job if you keep going this way. AC is not a DIY repair. Using a reman compressor instead of new will almost always fail and when it does it will take the rest of the system with it as you may have already done. Unless you are trained to recognize the problems when they arise, more damage gets done. You may think you are saving money but you are not.