Problem with screen flickering

[Kernal]

I recently built my first computer and it generally works fine except for one problem that renders the computer practically unusable when it happens: super-fast screen flicker.

Sometimes when I'm using the computer the display will suddenly start flickering extremely fast. I see horizontal lines where flickering begins and ends that flash quickly and change. Sometimes the screen becomes dim but readable for a few seconds with constantly shifting horizontal areas of bright or totally black areas.

Some things I've noticed about it:
- Generally happens when I first turn on the computer or am using it, it rarely happens if it's just on and idle.
- Happens while I'm in the OS (I'm using Linux) as well as during bootup and shutdown (even when the initial screen showing CPU and RAM information is up), so it's not an OS problem.
- Tried two different monitors (one CRT and one LCD) with the same problem.
- Tried two different cables to connect the monitor with the PC. Problem occurred with both.
- Not an outlet problem, as I tried two different outlets AND my old computer works perfectly in either of them whereas the newly-built one suffers the same problem with both.
- It is plugged into a power strip, but nothing else plugged into the same strip has any intermittent power problem.
- CPU temperature stays at 45 to 50 regardless of the presence or absence of the problem.
- CPU fan and all case fans are always spinning.
- Problem doesn't happen all the time, generally it occurs once a week for a day or so. After I noticed this I set up my old computer in the other corner, but it's annoying to have to constantly swap computers and although I have moved critical data to a flash drive, the computers have different OS'es and software and I have only one cable modem and set of speakers that I have to transfer between computers.

I think it might be the video card or power supply as both were fairly cheap components. Perhaps the card itself (which lacks a fan) is overheating or the power supply isn't giving it enough power? I don't have too many components in my computer, just one hard drive, a DVD-ROM/CD-RW, non-working floppy, and the video card in addition to the motherboard (with onboard sound and Ethernet), CPU, RAM, and power supply.

Do you think I should try replacing the video card and power supply one at a time, or could it be something else? I have PCLinuxOS on my built computer, no Windows. (I paid $140 for XP Home and then it didn't come with a CD key...)

[glc]

Detailed system specs, please - including power supply and video card brand/model. Brand, model, and age of the monitor, please.