Problem downloading exe files

I recently bought a Pentium III pc off of a friend. I later learned that the pc cannot download exe files. I am connected to the Net via a router. But as the previous owner had no router but had the same problem, I don’t believe it is the router.
I have no problems surfing, viewing and sending e-mails or using messenger.

I have disabled the firewall, lowered the privacy settings, re-installed IE 6, uploaded the service pack for IE 6, and have checked the settings in Internet options to make certain that the “download files” feature is enabled, and have even checked to make certain that no unnecessary plugins are resident in IE. All to no avail.

Help! I am at my wits end. Do you think loading XP SP1 would help?