It's not an IE problem. It's a file association problem. The items in Brink's post will fix it. You need to run all the ones for system files, exe, com, dll, etc.
I don't know what you mean about "verified their activation keys"....there is no such message associated with .reg files. I think you are doing something incorrectly.
Just had the same issue as AJBUB on my wife's PC (I use a Mac). Your fix worked perfectly. I assume malware was responsible for changing .exe extensions to prevent applications from running (no application would run, windows recommended internet explorer for all programs - even task manager); but after running anti-virus software, nothing was detected. Where else should I be looking?
Great advice. Ran both: ESET found nothing, but the Standalone System Sweeper found the malicious program "VirTool:JS/Obfuscator" . Took 2 hours and 47 min to scan everything. Very nice tool to have. Thanks for the scoop!