Huh... that's interesting.
Let's start with a little troubleshooting to get the obvious problems out of the way.
Open your start menu, and find "Command Prompt" under Accessories, or enter "cmd.exe" in the 'Run' box.
Wait for the black screen to pop up. Type in the following and hit enter:
assoc .lnk
Note that the above is a lower-case "L", not an "I".
It should return with this directly underneath:
.lnk=.lnkfile
If it came back with anything else, especially involving internet explorer, go ahead and enter the following:
assoc .lnk=lnkfile
It will return below ".lnk=lnkfile", confirming that link (shortcut) files are basically being directed to Windows' shortcut system instead of an individual program.
If that works, then congratulations.
If not, then we've got more troubleshooting to do...