On your E class at least, the battery in the key powers an infared transmitter to lock/unlock the doors. Try changing it.

Not sure about your other issues. Has the K40 relay ever been replaced?

__________________
Terry Allison
N. Calif. & Boca Chica, Panama

09' E320 Bluetec 77k (USA)
09' Hyundai Santa Fe Diesel 48k (S.A.)