Though you do not want to reinstall, I would proceed with the knowledge that it may end up being the only alternative.
Therefore recommend that you slave that drive to working computer and save needed files to a large thumb drive or other media. Should all attempts to save your install fail, you will have backup files to deal with a fresh install.
I see two main reasons for the problems you are having:
First deals with drive designations. The recipient computer may not recognize the new drive. Go to bias setup to make sure the drive is recognized instead of the one you removed. Also, check for drive designation (the CD-ROM may have been drive D in the donor computer while it is drive E in the recipient). Next make sure the the boot sequence is properly set.
Second likely problem would be that drive contains inappropriate drivers for the recipient computer. This can best be fixed by accomplishing a "Repair Install" - Instructions are here.
Of course, another possibility is to install Linux on that computer. My choice for an older computer is Linux Mint 10 or 11 32 bit version.