I suggest that you should REMOVE ONE (not turn-off) (AVAST or Zone Alarm).
You cannot turn off a software....but you need to actually uninstall it to test it.
There have been reports by many on the forum with conflicts of ZA firewall and Avast. I would start by uninstalling ZA firewall per the vendor's instructions, reboot your machine, and see if this fixes your problem.
You will, however, need a firewall since the XP firewall is 1-way and very weak. You might try something like Online Armor, Comodo (without AV), or Outpost to name a few. Avoid Ashampoo, which is a known conflict with Avast.
Let us know if this fixes your problem. Thank you.