both machines have a belkin wireless 54g network card within them.
But only computer 1 has an internet connection, I was wondering if there is a way to share the windows internet connection with my linux computer
First off, is your XP computer directly connected to the internet or do you have a wireless access point that it's connecting to? In the latter case, then I assume your Mandriva computer isn't associating correctly with the access point. In the former case, then you'd have to configure internet connection sharing with XP, though I'm not exactly sure how you'd set it up to do that wirelessly as I've never attempted to do that. I'd assume you'd have to set up an ad-hoc network so that the two computers could communicate amongst each other.
An alternative might be to purchase an access point. I'd highly recommend the Linksys WRT54G (but not the version 5.0 as that's crippled!) as it runs Linux and there are several projects that create firmware for the Linksys that add a plethora of functionality to this inexpensive router/switch/wireless access point.
Hope that helps!