Hello dbschmeck
Did you try booting your system in Safe Mode (when on battery) and then plugging the charger in?
Or
Is the laptop charging properly even after it automatically shuts down?
If you can successfully boot in Safe Mode with the charger, the issue might be with the configuration. (Highly unlikely)
If your laptop is charging properly after it shuts down, I would suggest you to give it a full 12 hours charge before you power it on again (first on battery and then plug in the charger after system boots), and check if the issue has been resolved.
If the problem is not resolved yet, it seems that there is some issue with the DC jack that is causing the improper contact with the charger pin.
In such a case, you may want to take it to an authorized service center to get the problem diagnosed and rectified by a professional technician.
Good Luck!!