Air Conditioning - Problems with A/C unit (outside)

I noticed today that the house was getting hot, and sure enough, the outside unit wasn't running, but the interior unit was.

I took it apart trying to see what happened. I replaced the fan motor a few years ago when it died, but that doesn't seem to be the problem. When I check all the wires, I didn't see or smell any shorts, nothing looks burned, the breaker is fine. When I switch the unit on, I hear a loud CLICK, and then nothing. I checked the wires with a power meter, and it seems there's electricity going to every thing, but I don't have a volt meter to see if there's enough power going to it. I looked at the capacitor, and other than a little rust, there's nothing visually wrong with it. There's no hum, no buzz, nothing.

**Edit** there is a hum at what I believe is the capacitor when the I switch the unti on and here the loud click. It's about every other time, so I didn't hear it at first**

I'm praying the compressor isn't shot, but I'm at wits end. It's a almost 20 year old Tempstar unit, so it shouldn't have crapped out this soon, I would think. Any help would be great, my wife has asthma and the hot stuffy air is hell on her, so I'm praying for a quick response. I can provide pictures of anything from almost any angle if needed.

Thanks in advance!

I have a feeling the contacts on the relay contactor are burnt and some slag is keeping them from closing. If you take it out, you might be able to remove the cover (if needed) and slip a narrow strip of emery cloth between the contacts and sand them down a bit. I folded a strip over and pushed it in with a small screwdriver, held the contact closed with my fingers and pulled the emery through. I did this several times to get them clean, but it worked.
Good luck.

http://i138.photobucket.com/albums/q280/LinetteF/AC%20Problems/HPIM0920.jpg

http://i138.photobucket.com/albums/q280/LinetteF/HPIM0913.jpg

I have a feeling that this is the culprit. It does make a slight buzzing noise when I try to turn it on. I will try replacing it tomorrow.

Yes the capacitor top appears to be slightly bulged in your pic so replace it.

Looks like the spade clip to the common terminal on the cap overheated a little, too.