I had a similar problem when I first got Win7. Though I do not claim to be a computer whiz, here is what I did to solve it:
0) With any luck, the archive is not corrupt or infected. Try it on a different, non-win7 PC if you have access to one.
1) Turn off UAC. Reboot. You may still have to manually find the winrar program and right-click it to run as administrator.
2) move the archive to a temp folder like C:\TEMP. So long as it is not in any of the folders directly associated with your user account (like 'Desktop' or 'My Documents') it should be okay. Sometimes, programs get denied access when trying to access any of the user specific folders and they don't handle it well.
3) If winrar installed properly, you should get an option to 'extract here' if you right-click on the file; do that. Double-clicking should work too, but make sure that when you hit extract, it doesn't default to any of the user folders or some deeply buried temp directory where you'll never find it.
I have also seen issues where older versions of winrar do not run well on 64-bit Win7. You may have to uninstall it and try with the latest version.
As a last resort, you could e-mail the file to me and I will attempt to extract it and send it back as a .zip that win7 can handle. PM me if you wish to go this route.
I hope this helps. Good luck.
~Daikhovalin