Hi and welcome to the forum. This is mainly UK based and the US gm volt may be better for you.
The original evse, the plug in brick, had a type 1 plug on it at the car end. It's probable the latch is not operating the internal microswitch.
Does the plug click into place? If not inspect both plug and socket for debris that is stopping the plug fully going home. If the latch is clicking then open the plug and check the microswitch.
If you have a electricty meter you can check there, you should see the consumption go up once the car gives you a solid green light from the EVSE, so uplug the EVSE check the meter, then plug in the EVSE and check the meter again, you should see consumption go up.
Solid green on the dashboard LED should mean it's charging. If you switch the car on and use the Energy button (just above the Start on my RHD UK Ampera, may be different in USA) the main display should tell you it's charging, and how long to wait to fill up.
But the original granny EVSEs are known to be flakey. If they fail they should be covered under the 8 yr/100k mile warranty.
Aargh, ok. In that case I thinka bout all that can be done is use a different EVSE to check it's not the car at fault; then check to see if there's any warranty left - My 2012 runs out this Sept! - get it to a dealer quick for a replacement if any wty remains. The original EVSEs with orange flex are a pain to take apart, and there aren't any user-serviceable parts inside, just a large PCB with lots of stuff on, and no circuitboard info available to debug. Worth trying a shot of WD-40 over the pins, or preferable a proper switch-cleaner spray, just in case there's a connection problem with the pins which can be fixed.
But I rather suspect it's dead/dying if it won't charge, and that means a new one. In UK I bought myself one from Evconnectors.com which can be set to 6/8/10/13/16A ! Something like that should be available in USA I reckon.