when i uninstall avast, still saying that my connection has a limited and no internet connection.
This means avast still left some remnants, or other (not avast related) issue is there.
What are your current and past other security software (firewall, anti-spyware etc.)?
Old security software's remnants could interfere with avast.
Each vendor releases their own uninstall utility, so try these tools to ensure there is no remnant.
After uninstall avast, try this tool:
http://my.opera.com/rejzor/blog/2013/02/01/avast-cleanup-toolAlso, I would check Device Manager with "Show hidden devices" on the View menu enabled to find there is no remnant of avast.
Most of avast! drivers are listed under "Non plug-and-play drivers" with "asw~" or "avast! ~" names.
As for the firewall, its device is also in "Network Adapter" category with "avast! Firewall NDIS Filter Driver".
Try to delete these items after uninstalling avast, and see your network connections restored.