The dash lights and the beeps from the car tell a LOT about what is happening - exactly what sequence is happening (left light? right light? all lights? lights flashing in sequence?), and the timing of the beeps given by the car will tell us a whole lot.
With the info I have, though, it sounds like the car isn't getting line power when it's trying to start charging. The EVSE is out there telling the car to charge, the car's saying to do so, but the car's not getting any power. When you turn the car back on, do you have the yellow "!"-car warning light on? If so, that's probably a problem with the charging port (if you've tried two different charging cables/stations), or it's a problem with the EVSE (if you're using the same on 120 and 240v).
Having it start and "run" for only 2 minutes is a sign of that, as it will time-out and throw the "!" error after 2 minutes.
The code that the technicians will pull (probably P3173, I think?) will have some reference to a "PEP" charging station that causes problems... but in reality, it's a generic error code for not getting AC power when the charging station (EVSE) is saying it's available.
100% gas-free since September 2012
2011 LEAF SL - Sep 2012~Sep 2014 - 35,737 miles
2013 LEAF S+Charge - Jan 2014-Feb 2017 - 68,065 miles
2014 LEAF SV+Premium+QC - Feb 2017-present