The windows firewall doesn't have the outbound protection enabled by default, so unless you enabled it then it shouldn't be getting in the way.
If you haven't done so already check out the link given by 'mchain' and ensure any remnants of your Trend Micro Titanium are gone. It is somewhat strange that this problem was also present with that installed.
You also said you have a previous 'glitched' version of avast installed, what was that version avast 5, 6 or 7 ?
Did this previous installed avast version allow internet browsing ?
It may be that this could be an issue and a complete clean reinstall should be done, see #### below.
####
- Download the latest version of avast, 7.0.1474
http://files.avast.com/iavs5x/avast_free_antivirus_setup.exe and save it to your HDD, somewhere you can find it again (if you didn't save your last download). Use that when you reinstall.
- Download the avast! Uninstall Utility, aswClear.exe
find it here and save it to your HDD (it has uninstall tools for 5.x, 6.0.x and 7.0.x).
- 1. Now uninstall avast! (using add remove programs, if you can't do that start from the next step), reboot.
- 2. run the avast! Uninstall Utility from safe mode, first for 6.x if previously installed and then for 7.0, once complete reboot into normal mode.
- 3. install the latest version, reboot.