yes, it is possible to install windows xp over an already installed/corrupt installation without formatting the hard drive. to do this choose the option given by the startup disk CD "repair a previous windows installation" you will find it should correct your current windows issues, however doesn't delete all your files, it does however move all your files under documents & settings, user, and may take a bit to find, because the direct path will not be there anymore. this will correct many windows issues, but if you find it does not correct them all, it is recommended to redo the win xp CD install & format everything. reason being is that many bugs & virus's affect or change your windows or registry files, sneaking their way into your bios configuration. in most cases, it is still recommended to backup important files to disk or CD, and format the whole machine with restore, clearing up things that would just be relocated with xp restore/repair.
I was also very hesitant to do so but it turned out to work floorlessly. It simply repaired and reinstalled default window components that might have been changed or corrupted. After the install and boot was complete windows ran brand new, not a single item touched even the background pic was the same.