The $.50 cent fixes are very rewarding, plus you learn a lot from them gaining something called 'experience'. Get enough of that and you can go pro!
Went through similar here with the central AC unit - building inspector was doing his thing (we're selling) and the AC wouldn't come on. Called in the pro, and he had it working in 10 minutes - found a bad t'stat connection in the air handler in the attic. An oversize wire nut had come loose, causing a bad connection. Replaced with proper size wire nuts (it's a pretty small wire nut for 2 of #18 wires). Spent the rest of his 1 hr min cleaning the outside compressor/condenser unit.
With the unit running, I find the unit is chilling the house like a meat locker - calibration setting on the thermostat had been offset by 6 degrees. We wanted 76 and it was giving us 70! Fixed that, then found that temps were coming down to the set point but the unit was still running. Found that the 'swing' setting had been set to '2' - plus/minus 2 deg from set? Changed that to .5 swing. I'm starting to think it's under control, but not sure when it went bad - seemed OK last year.
Gee, soon I'll get to move into a different house with different problems...