Classic signs of converter problem .. might also be a failed resettable circuit breaker http://www.amazon.com/420843-1-Resettable-Circuit-Breaker-without/dp/B002IV8ANS/ref=sr_1_9?s=automotive&ie=UTF8&qid=1457635550&sr=1-9&keywords=resettable+circuit+breaker which are usually located near battery.
Check the voltage at the battery with the rig plugged in 13.6+? If not then test whether the resettable circuit breaker is OK - if that checks out then you either have line issue or converter isn't working properly. Next step - get access to converter and check fuses - then check voltage (access may not be convenient but your going to have to access to replace anyway).