I want to thank everyone here for putting me on the right track. This started as a move from an ancient Intel Celeron system to a newer, but still outdated, AMD Athlon system. While I started out thinking about a video card as part of that move, you opened me up to the possible need for a new CPU. Well, when all was done on this AMD system, I now have a new Phenom II six core CPU, doubled my memory from 2Gb to 4Gb, changed to a new WD Caviar Black terrabyte SATA drive, upgraded by BIOS (to support the new CPU), and switched to a 64-bit version of Linux. I'm using the integrated HD3200 graphics. I had just recently added a new LiteOn DVD burner a few weeks back. This is all sitting in a nice Antec 300 case with an OCZ 600 watt power supply. I had incorrectly stated I had a Corsair or Seasonic power supply in this box earlier, that must have been in a different system I built, but I believe OCZ is a fairly decent brand as well.
Lots of things at play here with the multiple upgrades, but I went from stopping and stuttering YouTube vides at 360 or 480 in a small window on that Intel Celeron single core CPU, to the ability to watch flawless 1080p fullscreen on a 1920x1080 monitor. I think the biggest factor in that massive performance improvement was the CPU. It was $210 (total, before tax) for all these upgrades, which I think was a dang good bargain.
So thanks everyone for focusing me on what needed to be upgraded. I guess I had just gotten too tolerant of slow performance in my old age and didn't realize what I was missing. While I didn't "need" my computer to instantaneously render webpages in Firefox, now that it does, I kind of like it! I don't know where this new Phenom II CPU falls in "state of the art", I assume pretty far back, but still it was a great upgrade for me. Only $79 for that CPU too.