My ipod touch 2g is on the infinite apple logo reboot (I ran the Erase All Settings option while jailbroken ). The problem is that my home button does not function (a resistor burnt out while I had the ipod open to clean the screen, hence not being able to go into recovery mode. see picture: http://i34.tinypic.com/dwcjz7.jpg Everything had been functioning fine.

Itunes does not recognize it, nor does it come up as a USB device (it does charge it though). Am I out of luck trying to restore it with the broken home button? Is there a way to fix that broken resistor? Can I somehow bridge the connection so I can trigger the home button to get it into DFU?

i don't think you can do anything besides either try to fix the home button yourself, or go to a apple store, and get it replaced, because they can't tell if your device is jailbroken or not because its pretty much wiped out all memory and ... yeah they MIGHT give you a replacement.