All right, there are several things you can try. The first thing I would try would be to hook it up in the second computer and see if you can salvage any and all data you want saved. If this is an IDE drive, you'll need to set the jumper on the back of the drive to slave setting, and attach it to the middle connector of your IDE cable. I don't know the exact setup in your second computer, so if you have problems, let us know.
Once you have saved all the data you need, you can then put the hard drive back in the original computer and run a diagnostic test from the hard drive manufacturer. These tests are available online at the hard drive manufacturer sites, and can be burned onto a cd or dvd. They should be bootable. You can also use a copy of the Ultimate Boot CD, which has these tests among many others: http://www.ultimatebootcd.com/ Some of these tests are destructive to the data however.
You can also try to do a repair installation of Windows. This will require a copy of the operating system on a disk. It is possible to lose data on the hard drive doing this. Read this guide before trying this step: http://pcsupport.about.com/od/operatingsystems/ss/instxprepair1.htm