My HVAC stopped working. Here are the facts so what do you think?

It sounds like the contacts on the compressor contactor are fried. This can be caused by loose wiring, problems with the compressor windings, or a number of other things that can cause high amperage draw through the contactor. You'll need an HVAC tech to replace the contactor and insure that all of the wiring connections are tight. I would also recommend using a megohmmeter to check the compressor windings, and checking the amperage draw on both the compressor and fan motor.