Hi there,
I'm not sure about the Windows thing, I'm not familiar enough with the Media Center edition to help you.
As for the discs, the first thing I say to anyone that I'm working on their computer is "Do you have everything that is important backed up?"
I wouldn't count those recovery discs as backups if they didn't work.
I, personally, back everything up manually (music, documents, videos, etc.) by putting them in a temporary folder and burning it to DVDs. I reinstall all programs from scratch and copy paste all my files over. However, I keep all my files in one folder which makes backups easier, but if you don't, it's very easy to miss something, especially things stored withing the program files folders.
If you have everything backed up and all important files are safely stored on a disc or some other media, you could probably wipe out any partitions that are on the disc and leave it completely unallocated, or format it to the filesystem used by what the disc will put on. To be completely clear, leave the old hard disk untouched until your are positive you have everything you want off it.
Again, I'm not 100% sure on this, but aren't recovery discs just ghosting an image on the whole hard disk anyways? It would wipe out any corrupted files on the hard disc anyways if that is the case (I believe so anyways).