Nope, I'm not sitting on the throne while posting this.
Yes, I fixed my graphics card! After multiple failed attempts at being able to de-solder the bad caps, after giving up on the whole project a couple of times and after finding that this card still sells on eBay for north of $50 used, I went the brute force approach to de-solder and clean up the holes.
Finally at 2:00 AM yesterday I managed to de-solder the old caps (~20 effort hours), solder on the new ones (1/2 hour), installing the card (2 mins), hitting the power button (20 secs) and waiting for things to show up on the screen (20,000 hours), it happened. I finally got this card to work!
I had to literally drill the solder out of the holes after failed attempts at trying to get the solder off with solder sucker and desoldering braids (those videos on Youtube make it seem so easy). The older solder won't come off easy and when soldering the new caps, the new solder won't stick on easy! (those videos on Youtube make it seem so easy...wait didn't I already say that??)
In the meanwhile, last week, due to unknown/unrelated cause, the power supply also went kaput. eBay came to the rescue and I managed to snag one for 15 bucks.
So, I now have a working 7 yr old desktop....wooohooo!!!