Well this is a setback! After some forum searching, it looks like Windows computers cannot create official applications (read: games) for the iPod touch or iPhone. The modmyi.com forum summed it up best:
You can create jailbreak applications using the toolchain. Search is your friend.
You can not create official applications with the Apple SDK without a Mac.
I was under the impression that since the iPod touch was compatible with both Windows and Mac machines, the development kit would be as well. It’s not too surprising on Mac’s part, since their operating system probably foots a lot of the work for their dev kit. Observing the horrifying load iTunes puts on my Windows Task Manager (half a dozen tasks to replicate various Mac OS features), it is a small grace that their dev kit isn’t compatible.
Are there any ways around this? One possibility is to run OSX in a virtual machine, though I would need to own a copy of the operating system (estimated cost: $130). We shall see. Commenters, any advice?