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. For full details of the necessary browser settings please see the Configuring your Web browser for Content Manager Explorer section of the online documentation (login required).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!