Device will not power on or connect to PC

I am trying to repair an ipod touch 4th generation, 8gb. As soon as it is plugged it, it shows "critical battery" for about five seconds, and then the screen goes black. It will not turn on, or connect to a computer.

I've left it plugged in to charge for plenty of time, and tried swapping out the battery, with no success. Is there anything else I should try, or is this a lost cause?