Sounds like you may have several different kinds of 'Real-Time Protection' going on.
Try switching off this feature in AdAware and restart the machine.
You should repeat this process with the rest of the security you have installed, one-by-one, including Windows Defender and any firewalls (that goes for the Microsoft one too).
I've come across this intermittent problem before and ironically it was my security interfering with any network traffic rather than malware.
Hope it helpsEdit
Forgot to add that in IE8 you should:
Open Internet Options, Connections tab, click "Lan Settings" button,
deselect all ticks.
Edited by micksim, 10 November 2010 - 06:07 AM.