Apple logo flashes briefly when plugged in

I have a Nano that does not do anything when not plugged in, and when I plug it into the computer the Apple logo comes up very briefly (<1 second) before the screen goes black. It doesn't just do this once, though, it continues to flash on and off, as if it is trying to start up, but can't. I imagine that if it were a battery issue it would still work when plugged in. Is this a logic board or perhaps a connector issue? As of right now, my plan is to open it up and clean all of the logic board contacts with isopropyl alcohol and see if that helps.

Update

Simply cleaning the dock connector did not change anything. It looks like this Nano is going under the knife.