Hanging/non responsive programs when connected to the internet?

I've been having this problem for a while and it came out of the blue...

I load Windows 7 (64 bit) and after an hour or so programs accessing the internet stop responding (AppHangB1) such as Chrome, Windows live mail etc. I then have to restart my pc. I tried leaving my pc (desktop) for a few hours without a connection (via ethernet) and not a single hang/problem. I also tried leaving the internet connected with a browser or program running and it was fine.

I noticed last night that after it happened again (was watching a film on PC) the small monitor item in the task tray had a red mark through it, thus suggesting I wasn't connected to the internet . However, once I restart the PC everything is fine.

I ran Malwarebyte's anti-malware program and quarantined a few things but hasn't resolved problem.

I'm running the free versions of Zonealarm firewall and Avast anti virus. I suspect it might be one of these as I've had problems in the past with Avast.

Any advice/help would be greatly appreciated as I couldn't find anything on the internet about this problem.