It may be a small part in the condenser called a contactor. I would not call it a diy project (involves very high voltages) but it would not cost that much to get a tech to do it. If the system works fine otherwise, it is worth it.

Anyone competent with a vom can easily confirm a bad contactor.

Make sure you turn off the circuit breaker before you touch it, and check voltage. Amazon and ebay have them.

Are you going to explain how to discharge the capacitors so he doesn't go flying across the yard when he touches them?

https://www.youtube.com/watch?v=keM6kCfOsY8

Thanks to Dovetonsils for the lead on the contactor (in my non-HVAC-speak, this would be called a relay). After a little web-searching Friday based on his\hersuggestion, I was able to pinpoint the contactor as the likely source of the problem and yesterday I put another one in. All is peachy now!

For others with the same problem, I pulled the thermostat unit off the wall mount pins but the condensing unit continued to run, so I knew it had to be something with the circuit board on the air handler or the condensing unit itself. I then turned off the power to the air handler\circuit board, but the unit continued to run. At that point, it almost certainly had to be an internal wiring issue with the condensing unit.

After making sure the circuit breakers were turned off to both the air handler and the condensing unit, I pulled the quick disconnect (what I call the wall-mounted fuse cartridge). I then unscrewed the panel on the unit. I saw the two silver capacitors that looked like whiskey flasks, and with a couple of insulated screwdrivers I shorted out the contacts on each. No sparks were noticed, but I had read that the wiring in the fan motor would have essentially discharged the capacitors soon after the power was turned off. Still, it never hurts to be careful, or put another way, it can sometimes hurt when you aren't careful.

The contactor was obvious (I had seen a lot of pictures of it on the web by that point), and frankly a little disappointing in its simplicity. I took a bunch of photos of it with my phone from different angles, drew a diagram of it on paper indicating which wire went to what and how it was attached, and then labeled each of the wires with some tape ("upper left", lower right", etc.). Yes, this was overkill, but it was also new territory for me so I wanted to be sure to get everything back in the right order.

I unscrewed the sheet metal screws holding the contactor to the internal sheet metal, then with it in my hand I pulled off or unscrewed the wires connected to it. I could now inspect the contactor, and could see that the contacts (like automotive distributor points) were both blackened and melted in places. The spring loaded plunger that raised and lowered the contacts seemed to be fine though (my assumption was that the plunger itself had some sort of problem, but that didn't seem to be the case). My guess was that the heat from arcing from the points to the copper plate might have caused the areas of contact to stick to each other. Whatever the problem, the contactor had to be replaced.

I checked with all of my local hardware stores, appliance repair shops, and A\C distributors. Everyone was friendly and most had what I was looking for (a single pole contactor rated at 30 amps), but they all politely declined to sell me one, saying either that it wasn't an end user item ("not for the DIYer") or that they only sold to licensed contractors. I could see that these things are readily available on line and pretty standard in design. I was just about to order one when I happened to go out and get the mail. When I got to my mailbox I saw a truck owned by a friend of mine who has an apartment rental maintenance company. I explained what I was looking for and he said he had three on his truck. If I replaced it with a new one at some point, I could have one of his right now. Bingo.

I hooked it up in a flash, remounted it on the sheet metal, closed up the panel to the condensing unit, and then began to turn the power back on to the air handler and the unit. I turned the thermostat to cool, and heard the lovely sound of both the fan and the condensing unit kicking in. When that side of my house got to the desired temp, the thermostat shut off, and miracles of miracles, the condensing unit did as well.

Thanks to everyone else who provided advice. Unfortunately, I didn't see the answers until the morning, but all of the suggestions were sound one.

Happy (and cool) Sunday to everyone!

Nick in Palm Springs

"not a DIY part". Seems you proved them wrong.

I have reservations about selling parts to diy but if the guy has the old one in his hand and understands no refunds,I would sell it.

And he's still alive. Now check your capacitor as they go bad too. Lowes has the meter to check them MCF.