Lets give this a try, disconnect all the cables from the system and carefully disconnect the battery following this guide through step 4 [guide|5889]. Now carefully press and hold the power button for a good 15 secs to fully discharge the logic board. With the battery still disconnected plug in the MagSafe charger. The system should spontaneously restart, let it fully boot up and now do a problem shutdown. Reconnect the battery and put the cover back on.
That should clear the SMC lockup condition it that was the issue. Given the age of the system you likely need a fresh battery, install this gem of an App [https://www.coconut-flavour.com/coconutbattery/|CoconutBattery] which will offer a deeper view in your batteries health. Post a snapshot of the Apps main window here so we can see as well.
If the system still fails that is likely a deeper issue within the logic board.