Not solved unfortunately. I took the car into Smart Center for service. Turns out the car had never been serviced before and I bought it at 3+ years old 20k miles. They performed the service and did 2 required software updates. They found one of the same codes that the OP mentioned, P07800 – the precharging time of the high-voltage on-board electrical system is too long. The service tech wrote: NO INFORMATION FOUND ON THIS CODE, PROCESSED THE CODE AND TOOK TO PERFORMING SW UPDATE TO THE BATTERY. So basically they just cleared it and hoped the software update would fix it. They did a battery test and it passed the test no issues. Went weeks with no problems then a few days ago it came back but went away after 1 key turn. Now it's done it again 3 more times and been harder and harder to clear so it goes back to Smart next week. I'll post the outcome. Also when this is happening and I try to plug in the charger it won't charge and says Malfunction.
I am having this too. Just bought my 2014 used/lease return. Dealer was aware of BAP but they never sent the paperwork to Mercedes so now must sort that before I can get service. First 3 weeks 1K miles trouble free then did a short 20 minute charge while shopping and got the Drive Sys. – Engine off message. Plugged and unplugged the power cord and it went to ready and I could drive. Charged it fully. Next time different charger short 15 minute charge same message. Took 10 minutes of fiddling starting stopping to get it to start. Now it just happens randomly and so far I've been able to eventually get it to start. Once it starts it runs fine and I'm getting the full advertised range 3 bars of power. Now parked until I can get the BAP transferred to me and a service appointment. Hoping it won't need a new battery or that at least the wait time for a new battery has gone down. One month without a car will not be fun! Really disappointed as I'd done a lot of research and these cars seemed rock solid reliable.