In the worst case, it's still under warranty (all 7th gen nanos are still under one year from purchase).
So, you disconnect it from power, and it almost immediately goes dead? You can try a Restore... but it doesn't sound like the type of problem a Restore will fix.
You should probably have it looked by Apple Tech Support. If there's an Apple Store nearby, you can take it to the store's Genius Bar. To avoid waiting, you can make a reservation at the store's web page