Log in with your temporary profile if your account has administrative rights or with the local administrator account.
Start the registry editor and navigate to HKLM\SOFTWARE\Microsoft\Windows NT\CurrentVersion\ProfileList.
Look for the profile with the ".bak". This is the CORRECT old profile.
Rename the profile that does not have ".bak" by adding "_new" to the end. You can really add anything to change the name of this profile, just be sure to rename the profile with the matching SID. Next remove the ".bak" from the correct profile.
Log off and then log back in with the profile that was problematic. It is possible that Windows will undo everything you have just done and rename the profile again. If this happens you can try running a Check Disk on the partition that contains the user profiles. You will need to re-do all the steps above, run Check Disk, and restart.