In theory, the following procedure should work:
1_ Download
http://www.avast.com/uninstall-utility and the avast installer (so to reinstall anew after the procedure).
2_ Boot into Windows Safe Mode (WSM for short here).
3_ Uninstall avast using "Add/Remove Programs", if possible.
4_ Reboot again into WSM.
5_ Run aswclear for avast 7.
6_ Reboot again into WSM.
7_ Run aswclear for avast 6.
8_ If you ever had installed or updated from other older avast versions (like v.5. or even v.4.), then repeat the last 2 steps - ie the reboot into WSM and run aswclear - selecting each time each version of avast.
9_ Reboot again into WSM.
10_ Set Windows Explorer to show all "System" and Hidden" files, and to show known files' extensions.
11_ Search for any folder with a name containing "avast*" and/or "alwil*". For example, "Alwil Software", or "avast5".
12_ Delete those folders found in the previous step.
13_ Search for files starting with "asw*" inside "C:/windows/system32/drivers/".
14_ For each file found in the previous step, right click -> properties. If the file is from "Alwil" or "Avast", delete the file.
15_ Reboot into Windows Normal Mode.
16_ Select the setup.exe installer of avast. Right click on it -> properties -> UNBLOCK (if the button is not grayed out).
17_ Select the setup.exe installer of avast. Right click on it -> "Run as administrator" if such option is available. If it is not, the simply "Run".
18_ Once the installation procedure finishes, wait until the HDD led stops blinking "like crazy" (as oppose to blinking infrequently as usual).
19_ Reboot.
20_ After the first reboot, use the system as usual. Test it. Avoid rebooting immediately. Keep testing. No need for immediate registration nor avast accounts. Leave it for when all is fine and really working correctly.
21_ After a couple of hours, reboot and test if any strange quirks show up.
22_ Report back.