Just an update to this thread.
I've replaced the leaking capacitors with some Sanyo WG 6.3V 3300UF Super Low ESR capacitors, as you can see in the image below:
This wasn't easy at all. The solder points on the underside of the board are very small. It requires a very fine tip soldering iron and some steady hands. It's easy to make a solder bridge to some other point if you're not careful.
But everything went well because I took my time doing it. And I'm happy to report that I can once again over-clock my CPU. The BIOS thinks that my Athlon 2500+ is an Athlon 3200+. The results from a few benchmark tests confirm about a 35% improvement in speed. It's been running stable for 3 days now. No unexpected shutdowns, no BSoD, no problems at all.
I'd like to believe that the caps were the reason that I couldn't over-clock before. But something else may have contributed to the problem:
heat. While replacing the caps, I removed the heatsink from the CPU so that I had a little more room to solder. I noticed that the thermal pad or tape (not sure what it's called) between the CPU and heatsink looked kind of broken. Some of it had stuck to the heatsink and some had stuck to the CPU. When I tried to scrape it off the heatsink, it practically crumbled away. It had become dry and chalk-like. So I used isopropyl alcohol to get it completely off both parts, then applied some thermal grease (Thermaltake) and reassembled it to the board. Now, my CPU temperature is about 5°C cooler at 100% load, even though I'm over-clocked.
As I understand it, the A7N8X Deluxe will shut down if it determines the temperature is too high. So this could have been the problem all along. I guess I'll never know. But I'm glad I learned that lesson without frying my CPU. If I get a new processor and it comes with that pad or tape stuff, I'm going to immediately replace it with thermal compound. I just wish I had known this when I assembled my system four years ago. If anyone else is getting high temps, even with periodic cleaning, you might have the same problem under your heatsink.
Anyhow, that's the end of the lesson for today. I want to thank everyone who helped me out, especially Gibby. My system is speedy again, with the added benefit of being cooler.
TC