I can't believe the Mickey Mouse bad advice I'm seeing given out here.
So you have another computer you can get to, that's great. Because what you need to do is take the hard drive out of the computer that wont run, put it into the computer you are on now, and copy all of your files that you want to keep onto it. Dont worry about the adware infecting this computer, that's not very likely at all.
If you don't know how to do this, the best advice I can give you to try is to plug this harddrive into the same cable that the CD/DVD rom on the working computer is using. Otherwise, you need to learn about Master and Slave and jumpers on hard drives.
So your data is saved. Now to get an operating system back on your other computer. That part isnt so easy without an XP installation disc, and I have no experience with an upgrade disc so have no idea what to suggest there. Other than to get one any way you can. You can forget about the existing installation being fixed, it's not worth the time or trouble, a clean install is the best thing you can do.
It isn't likely the system is going to boot to an upgrade disc, try booting to the ME install disc and go from there.