Something must happen. When you open a command prompt and enter regedit, what happens? Are you saying the prompt returns without any message at all? I would expect, at a minimum, it would return a message saying something like "command not recognized".
Look in the C:\Windows folder. Is regedit.exe in there?
It might be possible that malware or a trojan horse got on your system and replaced regedit.exe with something bogus. Have you tried running a virus/malware scan?