Is this your XP or Vista system?
Have you tried running Firefox without Add-ons? I believe you can do this by clicking on the FIrefox button at top left, then Help then Restart Firefox with Add-ons disabled.
If no problem then one of the Add-ons is the culprit, though this seems unlikely since you say it also happens with IE. If, for some strange reason it does make a difference then you can use Firefox / Add-ons to find the one that is causing trouble.
You can also do likewise for IE, by starting it with no Add-ons via Start, Accessories, System Tools, Internet Explorer (No Add-ons).
Even though ESET says it's not a firewall problem, I still think it would be worth while uninstalling ESET and testing to make sure. Perhaps install Microsoft Security Essentials while ESET is uninstalled for safety?
Edited by Ztruker, 06 July 2012 - 05:27 PM.