I found a 2.1 amp charger and the original cable solved the problem one day, and plugging it into my PC USB port to waken it up before charging with a charger solved it another day.
The Nexus 7 battery runs down even after "shutdown" much faster than my iPad which is annoying, and the "Totally dead Nexus" problem makes relying on it problematic.
If used regularly and charged regularly it is a great machine, but Apple's much better connector and battery make it more reliable as far as I am concerned.