I have Windows XP SP3 32-bit, and Avast 7.0.1474 is working fine. I uninstalled previous version, and ran the Avast Uninstall Utility too.. and then installed the latest version.
As the member above me wrote, it sounds like a problem with your system. Maybe the Zone Alarm firewall is causing trouble. I have read one other person report about having problems with Avast install on another site, and he was using ZA too. He removed ZA, and then installed 7.0.1466. All running good. I have reported to him that latest version too is working good, so most probably, he will go for it.
Any other security software you have installed, which might be interfering with Avast?