I am using a fairly old machine-- Pentium II 233, Windows 98, that was pieced together seperately.
Last night upon startup, it went to the Windows 98 screen, then went through a self diagnostic test (checking for lost clusters, searching directory, etc), and started up normally. After successfully burning a cd the screen went tye dye. I restarted and the machine went through another self diagnostic, but this time did not start up, but went to the tye dye jumble of colors. Then the screen would black out for a second--like it does when you change video settings. Now I am unable to get to my desktop at all.
I wondered if this sounds like a software corruption, hard drive, motherboard, video, etc. problem

Sounds more like a video card problem than anything else. Software such as drivers usually works or it doesn't - nothing in between.
I'm assuming it's using a PCI graphics card - If so, open the case and check to see if it is seated ok. Another obvious thing is all the external connections (cable). If things seem to be in place, try putting the card in a different slot, after giving the slot a quick blast out with compressed air. A cleaning compound (usually a high-alcohol base) can be used on the contacts, but make sure you follow all the usual ESD rules if you choose to do this.

Is it possible for you to boot into DOS? can you boot into safe mode?
let us know if you have tried any of these.

Hello andyman,

Welcome tohttp://www.pcguide.com/ubb/pcgubb.gif Forums!

I see deddard beat me to the punch here...:D I would agree that it seems to be the video...

I would also suggest an attempt at DOS...using a Win98 boot disk and see if you get anything on screen.

If so, just as a matter of course, I would run the Harddrive diagnostics which are available from the manufactuer's web site and also a Simm Tester...my version of checking the radiator level and battery connections on a PC...;)

I know the moniter & connections are okay because I see the usual DOS readouts upon startup (Pentium II 233, memory, & cards installed), also I get the Windows 98 screen, which I assume wouldn't be visible if the graphics weren't working (though I don't know).
It's when the desktop is supposed to appear that the problems start.
How do I start in safe mode?

Press the F8 key before the Windows 98 screen appears. This will give you a menu from which you can select safe mode, and step by step among others. Try to start in safe mode first. If this works, then use step by step. If the problem is a corrupted driver, this will help you identify which one it is.

Got the machine to start in Safe mode, after which I retarted to find everything working like normal for a while. Then the moniter blinked out for just an instant, as if it lost power, and the whole thing froze. Now it crashes before the RAM check is complete (with just some colored blocks appearing on the screen, and no apparent action from the hard drive), so I can't use the window's startup disk, can't start in safe mode.

You need to try another known good video card.
Variable

Reboot,press F8 before Win 98 Screen to enter Safe Mode and then run scandisk and note if there were any errors. After scandisk run the step by step option in Safe Mode as Jhorner1 suggests. If there is a software problem that keeps you from being able to start booting windows it should show up here.

Got the machine to start in Safe mode, after which I retarted to find everything working like normal for a while. Then the moniter blinked out for just an instant, as if it lost power, and the whole thing froze. Now it crashes before the RAM check is complete (with just some colored blocks appearing on the screen, and no apparent action from the hard drive), so I can't use the window's startup disk, can't start in safe mode.

sorry, didn't mean to repeat myself;)

Think I discovered the problem. The computer works fine after being unplugged for a while. I noticed the fan on my power supply is not working, and I think it overheated. New power supply is almost always the easiest solution! Thanks for the suggestions