When I tried to install Avast on a Japanese WinXP SP2 Home PC, I got the 1006 (000003EE) error. I was trying to run the installer from the Desktop. I noticed that WinXP uses Japanese characters for the Desktop folder name. I then created another directory and gave it a name with English characters. I moved the installer into that directory, and I had no problems running the installer from that directory.
Please, post the last 200-250 lines of avast log: C:\Program Files\Alwil Software\Avast4\DATA\log\Setup.log
Tech, it is known problem. Cyrillic letters somewhere in the path Avast! doesn’t like too 
Workaround is simple - use only English letter in the path.
Same error in Windows 7 (64 bit)
There is no log file.
Peter