Well first of all dont worry about not backing up - the Windows Repair doesnt touch any of your files so if it never finishes and Windows doesn't boot you can just shove the HDD in another machine [as slave if IDE] and get your stuff back.
Since I think you have a hardware problem I would probably see about getting your files back asap in case it is your HDD.
My first action would probably to reformat the HDD and reinstall Windows and see what happens. If all is well then it will probably have been something wrong with your previous install.
If you have trouble with a fresh install next step would be to test your RAM using something like
Memtest86. If you have a RAM problem this should find it. I would leave it running overnight to be absolutely certain but any serious problems should show up pretty quickly.
If your RAM passes Memtest all I can think of is trying another HDD and see if you have success with that.
Assuming all the above doesn't turn up a problem it could be something to do with your motherboard or CPU - possibly even your DVD/CD-ROM drive, though I am not sure how this would nerf a Windows installation.
This post is assuming it is a hardware problem so I would probably wait for some more answers off other members before going on a mission. It may well be a software issue that I have considered.
Hope this helps
SiriusB