Ok, I think I may have an answer for you, and at first, may seem quite odd. But only a few weeks ago, I was experiencing almost identically the same problems you are experiencing right now.
My hard drive had crashed (I had left the computer on one day and when I came back that night, I had a blue screen of death). I couldn't access anything on the hard drive..when I rebooted, the computer seemed much slower. After getting to my desktop, I'd open something like MS Outlook, or Explorer, or some other software, and within 2 minutes, the software would close down (almost as if the computer was shutting down). Shortly thereafter, I'd get the blue screen of death AGAIN!
I tried reinstalling Windows a number of times, knowing that there was very little I could do to restore the data until I got into a Windows environment. (I needed internet access!) Everytime i tried installing the OS, certain files would be missing or corrupt during the install. I thought there must be major problems with the CD or maybe the hard drive. When I finished the install, it would reboot the computer, go through all the startup tests, and once it tried loading windows, it would conk out again.
I just so happened to be installing Windows on another friend's computer so I used the same CD I'd been using for my own install and there were no problems at all... so this was obviously a HD problem...
Luckily I had a few extra drives lying around so I did a switch.. When I opened the case, I realized that the inside components were quite warm to the touch (including the hard drive itself!)
Anyway, I did the switch and then tried reinstalling windows (this had been the 5th time I tried reinstalling - I even tried installing an old copy of Windows 95 just so I could get into a Windows environment, but I had similar problems with that). So even when I switched drives, this did not resolve the problem at all. The problems continued and they started getting even more bizarre as time went on.
After about 5 or 6 days of trying everything and anything I could imagine (I even switched the power supply thinking that my system was overheating and preventing the components from working properly), I got fed up and took it into a local repair shop.
When they called me and told me the problem, I almost died. It was the last thing I was even considering... It was my RAM chip. After they had performed tests on the 512 MB chip, they were able to identify corruption errors at the 1MB - 4MB level. And this made so much sense. I couldn't figure out why I had no problems running anything in DOS. I had used a million and one utilities in DOS and didn't experience any problems. It was only when the system tried to go into a Windows environment (regardless of the OS version) did these problems present themselves. The fact is that Windows requires the use of memory slots about the 640k memory barrier. As soon as it tried loading Windows, it would attempt to access this memory above 640K and right away would start becoming symptomatic.
If I were you, before going out and replacing a hard drive, I would consider testing your memory chips. As long as you can get into DOS, you can do this. There is a program called Memtest86+ which is an advanced diagnostic tool for testing memory modules. On your other computer, download the pre-built ISO image from http://www.memtest.org/,
run the image on a blank formatted disk and then bring the disk to the failing computer and load the computer with this disk, just as you would with any other boot disk. You'll be able to run the tests from this disk. If there are any problems whatsoever, this program will tell you.
The reason why I am leaning towards the fact that it's probably a memory problem is because of the remarkable similarity between what happened to my system and what is now happening to yours. Also, you've conducted a thorough disk check that indcates there are no problems with the disk. If there really was something wrong with the disk for it to cause such substantial symptoms, then the disk check software would have found something (it might not have been able to fix it, but it would have found it). Also, since you can't seem to keep Windows open, then that's pretty indicative of a failed memory or power supply problem (usually with the power supply, the computer would automatically reboot itself as it couldn't keep enoug power to run all the components in your system and this would happen in DOS and Windows, not just the latter).
Hope this helps....I wish I had known all this before I had gone through so many hours of troubleshooting and the cost to hire a tech support person. If this is your problem, atleast you'll be able to replace the memory for cheaper than you would a hard drive (in most cases).
BTW, if it is your memory, I would also check the manufacturer's website for the warranty and gaurantee policy. Most memory manufacturers have limited lifetime warranties and will replace defective memory modules (even if it's from a power failure).
Let me know how things work out for ya!