Before we start, perhaps a little detective work is in order: create a new user account and log in as that to see if you get the same problem. If you don't then you have corrupt profiles - simply save all your settings, log in as Administrator, delete the profiles, and log in again as yourself and copy back your settings (not ntuser.dat).
What exactly within your profiles are you worried about losing? Your profiles should be stored within c:\Documents and Settings\ so all you need to do is log on as Administrator then copy them elsewhere. You should do this and back up the Registry before any messing about. Within Internet Explorer you can export your Cookies and Favourites to files. The reinstall you are considering is called an Upgrade Install - XP should detect that you have a copy of XP and it's not the same so it will ask you if you want to upgrade it. This will preserve most application and Windows settings. However, this means that the problem is likely to persist! This is also non-reversible.
If you have the time and the disk space, a better way is a non-destructive reinstall.
Prepare all your CDs and utilities. Double-check that you have all serial nos etc. I tend to have everything in a directory c:\install. If you're running FAT32 and have a DOS7 bootdisk available, copy the whole XP CD to its own subirectory (e.g. c:\install\xp); advanced users may like to take the opportunity to slipstream SP1, add extra drivers, etc. One oft-used system is to have all your install sets on C: as a FAT or FAT32 partition - not necessarily bootable - but have D: as your XP partition running NTFS.
Save all your settings as above.
Save all your application settings (this varies per application).
Boot the CD to a command prompt (the Recovery Console).
Rename c:\Documents and Settings
Rename c:\Windows\win.ini
Rename c:\Windows\system32\ntoskrnl.exe
Rename c:\Windows
We now have an OS that will not be picked up by the reinstall process but can be made active if needed.
If using a CD boot from the CD and install XP from scratch.
If using a DOS7 boot disk, boot from the boot disk and run c:\installdir\winnt /s:installdir. It helps to have HIMEM.SYS and SMARTDRV.EXE loaded but is not necessary (there are other command-line parameters which may be of interest). XP will now install.
Reinstall all your apps. Because most of the files are already in place, this should be much quicker than installing for the first time. Some apps (e.g. XNews) may not need reinstalling at all.
Set up your users and copy back the necessary parts of the old profiles - indeed you can simply copy back your old profiles if they are not corrupt (if this doesn't work, simply delete the copies).
Restore your application settings.
If it all goes horribly wrong, simply boot to the command line, rename the new installation directories and un-rename the renaming you did to start with and you are back to where you started with no harm done.