So I finally bit the bullet and decided to update my power supply and video card. Specifically,
Power supply: ModXStream-Pro, 600 W
Video card: XFX Radeon HD 5770
The PSU seems to be running just fine. I removed my old card (GeForce 7600), uninstalled the drivers, disabled the onboard driver (GeForce 6100). I have downloaded and installed the drivers for the new 5770.
My mother board is an Elitegroup MCP61P, old and crappy but it does have a PCI-Express with X16 lane, so I think it should work.
The card is installed, and I connected a power cable to it. Currently, the PC is not detecting it at all. It's not listed under the Device Manager or Belarc; they both only list the 6100. The monitor is working fine if I plug it into the standard monitor port. If I plug it into the card (using a DVI-VGA adapter), nothing.
IOS Game Center ID: Isotope-X