i had an iPod die this way, unexplicably.
i ended up getting it replaced out of warranty, by the nice people at my Apple store.
after the fact, i found that there is one alternative that has worked for some people. you say there is NO way to jump start it externally, so the answer lies internally.
all you have to do is open it, disconnect the battery, and reconnect it.
here are some of the best pictures and instructions i have seen if you're up to the task. (you don't need to take it all the way apart as the pictures show) if you search around on the internet for your problem, this is what everyone insists is the only thing that gets it back to life.
otherwise, apple's your only hope of resurrecting it barring any divine intervention.