Can I save this 2016 500e 33k miles?

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.

Then 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...:


...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.

Oh, wait! Orange Coast Fiat is less than 30 miles from me, so if the odometer is flashing I can meet you there with my MX+ & yellow adapter.

But meanwhile you should also check/clear codes in the On-Board Charging Module in the Battery Management section of AlfaOBD, because of the very last line below...:

• Nearly all failures have been from a low 12V starter battery.

• Nearly all the rest have just been from a computer glitch (often from the humidity sensor) creating a false alarm that makes the computer think it's unsafe to start &/or charge. The car works once the error code is cleared with OBD &/or battery disconnect reboots. The contactor disabling glitch was only discovered a little over a year ago, & gives many if not all of the symptoms of HV pack failure, so likely many of those warranties were unnecessary.

• Only 1 or 2 failures were definitely from:
  • One or more weak cells in the HV pack. You can't check for that until it charges to 100%. It's usually from long-term storage/shipping without charging, or from failure to get U69 done before it causes damage, & you can't check for that without maintenance logs, because Sept 13 2018 is just the issue date.
  • A bad PIM &/or the DC-DC converter it contains. ~$6k new but a used one works.
  • A bad BPCM inside the HV pack. The one I remember had pretty low miles, about like this thread's subject line. There's a guy in Poland who knows how to fix that part.
  • A bad OBCM. The one I remember had about 90k miles & I think the other one was plugged in during a lightning storm. That's about $2k new, installed.

Summary:

1. With car asleep, leave humidity sensor unplugged, disconnect 12V, check HV fuse continuity, reconnect it after 5 min*, then reconnect the 12V.
2. Following onscreen key position instructions*, clear all codes (BPCM, PIM, OBCM) & if odometer is flashing do proxy align* until shows "Finished" (mine took 3 tries).
3. Confirm 11.6+V at the wires, try OEM charge cord & if it doesn't work, check "Minimum Cell" in BPCM status section (not the faults section) for 2000+mV (or better yet, 2700+) & if it looks good but there's no clunk, try contactor reset.

*1. If possible, do a 30+ hour disconnect before even bothering with steps 2 & 3.
If not, & none of the above works, then try 30+ hour disconnect & repeat steps 2 & 3.

*2. Turn the key only 1 click to "mar" before connecting OBD. 2 clicks might make it think the "engine" is running. Proxy align sequence: