If you are using a ClickOnce extension in your (non-IE) browser, the I'd strongly recommend that you try installing this from Internet Explorer instead.
You could also try:
Ensure that the URL of the Tridion Content Management Explorer (CME) is in (at least) the
Trusted SitesorLocal IntranetZone in Internet Explorer.If that doesn't work, then try disabling your antivirus program (temporarily) whilst you try to install Template Builder.
If that still doesn't work, then you may want to consider using CCleaner (or similar) to cleanup the registry.
Please note that normal common sense rules (backing up, etc.) apply when trying items 2 or 3!