Updated CPU driver for MSI motherboard, as well as onboard LAN driver and some of the software utilities that came with the motherboard. Now I'm getting errors with LiveUpdate (MSI's updating software), and the performance is not any better. BIOS and NB chipset drivers had no updates available.
Interestingly, the voltage for CPU, AGP, RAM, etc, are all 5-10% below target. I'm pretty sure they are within allowable tolerance, but it just reinforces the theory that the PSU is contributing to the problem. I would think that if the Video card had insufficient power that it would just fail to work, but it's a pretty sophisticated card and I wouldn't be surprised if it scaled back its own performance to match the capabilities of the PSU.
New PSU is in the mail from newegg (CORSAIR CMPSU-520HX 520W ATX12V v2.2 and EPS12V 2.91 Power Supply 100 - 240 V UL, CUL, CE, CB, FCC Class B, TUV, CCC, C-tick - Retail). Hopefully bumping up from a barebones 350W PSU to a decent 520W PSU will make a noticeable difference. But at $119, my "cheap upgrade to extend the life of my old PC" is now topping the scales at $260. (Note: Theoretically I have $40 in mail in rebates coming my way, but I never count those as I only actually get about half of the ones I submit)
The video card is "exchange only", meaning I'm stuck with it. The PSU is a standard return item, so I can send it back for a refund if necessary. I figure that if I end up biting the bullet and buying all new parts for a whole new system (PCIe here I come!) then this PSU will be a nice addition to that system. So, it's not all in vain.