The operation was a success!
The failing caps were "Elite" brand, and while they were a nice color of navy blue, they weren't built to last. I also spotted a bulgy G-Luxon 10 volt 1000 microfarad cap that I had missed before, so I replaced it with a 16 volt 1000 cap salvaged from a dead motherboard.
When I initially tried to power it on, I only got fans, no POST beep, and no display. I was very disappointed, but I didn't give up. This board has slots for SDR and DDR, and I had tried a 512 of Kingston PC133 I had nearby. So I then tried a 512 of PC3200, and it POSTed!
I initially was going to install Win98 on a 250 gig SATA drive with an adapter, but the board couldn't detect it. But it was able to detect a 120 gig SSD, so I used that instead. Since installing Win98, I found a BIOS update, and it can now detect the 250 gig drive.
When I had the heatsink off, I discovered that the 1.8 GHz CPU is actually a 2.4 533 MHz FSB one. I wonder what they had where that was a good upgrade (maybe a Celeron, so they at least jumped up to 512 cache)? I had a 2.53 533. so I'm up to 1.9 GHz now. Does anyone reading this know if a 2.8 GHz 400 FSB would work in this motherboard? The manual says up to 2.2 GHz, but no doubt these 533 FSB chips aren't supposed to work either. There's one for pretty cheap on Ebay, I might just try it and see.