I once had Firefox refusing to run, and I had to delete the Firefox user profile. It survives a Firefox uninstall/reinstall.
It seems to be a fairly common bug.
A profile in Firefox is a collection of bookmarks, browser settings, extensions, passwords, and history; in short, all of your personal settings. These items are stored in a special profile folder on your hard drive. Each user has one of its own.
In Windows XP, it is located as follows:
C:\Documents and Settings\<User Name>\Application Data\Mozilla\Firefox\Profiles\xxxxxxxx.default\
The xxxxxxxx is simply a collection of 8 random numbers and characters, used to ensure that each profile is unique. Firefox automatically creates this. When Firefox is in use, it locks the active profile to keep other programs from altering the contents or causing conflicts. This lock is normally transparent to the user, but sometimes the profile remains locked when it's not expected.
You may not have to actually delete the profile, you may only need to delete a file called parent.lock which may be in your profile folder.
So I suggest you follow these steps (They may work)
Give your regular user account its admin privileges back.
Log in to that account and do not start Firefox.
Check in Task Manager that Firefox is not running.
Look in the profile folder for that user and see if parent.lock is present. If it is, delete it.
Now try running Firefox.
If it does not run, you could try the scattergun approach of backing up everything in the profiles folder (by copying it all to another folder) and then deleting everything. If Firefox starts up OK, then you could copy back your bookmarks.htm file, etc.
For a discussion of the "Firefox Profile In Use Bug" see here
http://kb.mozillazine.org/Profile_in_useand here
http://www.talkgold.com/forum/r117316-.htmland here is a detailed account of how to create and use a new user profile using Firefox Profile Manager
http://www.borngeek.com/firefox/profile-tutorial/