That's exactly what you need to check, because when the HV pack is dead like this one, charging is the only function available.
However, since the dealership should certainly have tried plugging in, the first thing I'd do is make sure it's asleep: Key off for 2+ minutes during which you don't open OR close either of the doors or the hatch (since any of those movements wake it up). So to disconnect anything, leave at least 1 door open for access.
Then leave the humidity sensor unplugged, just right of the rearview mirror. Click to enlarge:
Middle fingers in each of the upper openings, pull perpendicular from the glass, round
toothpick kept parallel to glass, pushed straight in to wedge the black socket open & pull the purple plug. If the sensor isn't there because the glass was replaced with the gas model part, dig around under the headliner, since that's where they usually leave it plugged in.
While it's still asleep, I'd disconnect the 12V battery, then disconnect the HV fuse under the back seat for 5 minutes, check its continuity:
Then reconnect it carefully (note the last 3 pics) & then reconnect the 12V.
Then clear as many codes as possible, especially in the Battery Pack Control Module in AlfaOBD's "Battery Management" section, & the Power Inverter Module in the "engine" section.
Then I'd check the 12V starter battery for 11.6V or more at the wires
, not the terminals, in case there's a bad connection.
I'd plug in, preferably to an OEM cord that was just plugged in, with the 4 lights going green one at a time, & the 2 lights going from red to green as shown:
If it doesn't make the "clunk" sound in the vid here...:
This is the normal little "clunk" sound a 500e makes right after plugging in.
...then check the current min/max voltage as follows, not like in post #1, which appears to have incorrect data (click to enlarge):
Then scroll down & send us a shot of this, minus the red I added:
AlfaOBD shows that the car's low voltage "warning" & "alarm" levels are both 2699mV, so if the min is above that it should allow charging. I'd think that it might allow charging even at its "emergency" level of 1999mV, but I'm not positive.
I am positive that the car won't start or charge if there's no clunk, so the next thing to try is a contactor reset:
If that still doesn't work, the last thing I can think of right now is that some owners have tried everything & then left the 12V & HV disconnected for 30 hours & then it worked after clearing codes again.