Did you charge both the Dock and Tablet for about 8 hours to begin with? If so, maybe your charger is defective? It sounds like your tablet battery is dead (and probably the Dock too). I would plug your charger into the tablet only and give it a few hours to see if it charges. I'm not sure if the Prime works exactly like the TF101 but with mine when the Tablet is attached to the Dock, the charger is plugged into the dock and eventually both will charge up. Then after the charging is complete, the Dock continues to charge the Tablet until it is down to 3% then the Tablet exhaust it's own battery.
Once you get it going again, get Dual Battery widget from the Play Store so you can see what's up at all times.