What version of Avast are you using? What is your OS? Is your Firewall blocking anything related to Avast and what is your firewall?
Have you tried an Avast Repair?
- Control Panal
- Add/Remove programs -> Avast
- Click on Repair
- Follow instructions
- Reboot
When you uninstalled, did you use the Avast Uninstaller Tool in Safe Mode, then reboot?
Are you using any other security software now or in the past? If in the past, was it removed by the vendor's tools, or another way?
Edited: Additional info. requested