Fine. Gotcha. Above when i referred to IE I meant Internet Explorer. Try it and report back. for example, if you type c:\windows into the IE address bar then you should see the files and folders inside \windows. Is explorer.exe there? And if you enter C:\windows\system32 you should see winlogon.exe [you must have that, cos otherwise you would not have been able to restart your sys].
Actually, they both should be there because the moment BDF deleted those two at your behest Windows File Protection System should have replaced then both. Obviously your sys does not have a backup of explorer.exe. You could check that by entering into IE address bar:
c:\windows\servicepackfiles\i386 -is explorer.exe there? [you will only have that folder if you have upgraded a service pack, eg SP2 to SP3].