Avgw.exe is a legitimate program for the anti-virus, and allows it to run in the background to check for viruses. Unless the file is somewhere on your computer it should not be, it is beneficial rather than harmless. If you do not want this kind of real time on-going protection, you could disable it, presumably by turning of its "resident shield."
You have already posted a HJT log for review by our team of experts, who may find other malware causing your problem. To avoid duplication of effort, and perhaps cross-interference, I suggest further replies await the outcome of the team review.
Edited by jgweed, 06 March 2006 - 07:58 PM.