I followed the suggestions of others, and used the Console Recovery from the install disk to copy userinit.exe to wsaupdater.exe, but I didn't get any results with that. I finally did a repair install from the Windows XP disk and that allowed me to log in.
I didn't see wsaupdater.exe in my system32 folder before, but it is there now. I'm wondering what I should do at this point to avoid the problem that I had before. The description for wsaupdater.exe is "Userinit logon application", so I think if I just delete it, it won't let me log on again.
I opened the registry editor and went to "My Computer\HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows NT\CurrentVersion\Winlogon". The Data for Userinit is "C:\WINDOWS\system32\userinit.exe,userin". I'm not really sure what I'm looking for, though...
I just want to resolve any potential problems that Wsaupdater.exe could cause in the future.
Any help would be appreciated!