Look in Control Panel, WIndows Firewall and see if there is an exception for "Apache HTTP Server".
If there is click edit, then make sure the path points to your XAMPP install
If there isn't one - Add one using the Add Program
or you could try the Add Port option - Name it Apache, and make it Port 80
Beyond that I am mystified...
Maybe I missed something totally obvious.
You could also try installing WAMP - it won't cause a problem as long as you disable Apache and MySQL as services in teh XAMPP Control Panel first.
If it won't run, its for sure a wierd 'machine' porblem...
If it dows run, you know its something odd about the XAMMP install.