George Schwanauer, The battery, cable/charger or charge port may be faulty damaged. Look in the charge port and blow/pick out(carefully) any dust/debri that may be causing an issue also look in the port for any bent pins and straighten very carefully with a tooth pick. Try a different compatible charger/cord to see if that is the issue. If different compatible charger/cord does not fix and port looks/test good, the battery or connection could be bad, if able to clean battery connections( clean with Qtip dampened with 90%+ Isopropyl Alcohol) and reconnect/install battery, still not charging battery probably faulty. Below is a link to show how to partially disassemble the phone to check some components and replace battery if need be. Good luck. I hope this helped you out, if so let me know by pressing the helpful button.
Samsung Galaxy Tab 7.7 Battery Replacement