Well, I'm certain that we've had a lot of people playing on Win7 - especially the 32 bit version should be no problem at all. I was actually hoping you'd say Win 8, because that's the system that's been tried the least.
I'm not sure what else I can suggest to help you. Most of the time, when a problem comes up, it's a problem related to playing the game - I think this is the first major problem ever reported for the installer. Maybe PopsiclePete will be able to suggest something, but you'll likely have to wait a couple of days for that, because I don't think he visits the forums that frequently these days.