Nice logs with some problems, esp. with IE. Do you or did you at some point have a variety of antivirus software like Norton Internet Security, McAfee, CA, Kaspersky, Panda, Sophos, Trend, Ahnalba? Do you or did you at some point have a variety of firewalls like McAfee, Panda, Symantec/Norton, Tiny, Trend, ZoneLabs?
Essexboy will review the logs, since he is the expert and contact you with further instructions.
In the meantime, I want you to:
1. Update Avast and scan, and update MBAM and do another scan for possible disinfection. If anything shows up as positive, please post the infection results.
2. Download
CCleaner http://www.piriform.com/ccleaner is a freeware system optimization, privacy and cleaning tool. It removes unused files (cache, temporary Internet files, etc.) from your system - allowing Windows to run faster and freeing up valuable hard disk space. It also cleans traces of your online activities such as your Internet history. Additionally it contains a fully featured registry cleaner. Remember
when installing to uncheck the Yahoo toolbar. Don't use the Registry cleaner until your problems are fixed by Essexboy.
You're system needs a lot of cleaning up and updating of software. Once everything is fixed, you should download the free Secunia Software Inspector to keep your software up to date
http://secunia.com/vulnerability_scanning/personal/ and use it weekly/biweekly.