Had this problem after initial install of keyless remote system. The unlock pulse signal was to short, had to set unit to provide a longer pulse. After that, all has been well for 4+ years.

Your system may have been on the ragged edge of pulse length. As to the pump, for a left hand drive car its under the passenger side rear seat. Is your Keyless control unit there or in the driver's door (or under driver's mat)? Moisture could have affected it.

On the other hand, since it does the same with the key, I'd troubleshoot the electrical switch and wiring on the drivers door lock cylinder. Procedure is in the service manual.

Note that $750 is more than a bit extreme to replace what is not the problem based upon your post. You are getting ripped.

__________________
Hanno
'79 6.9 Sold (after 27 years)
'83 280SL, 5 spd.
'94 E320 Sdn. 5 spd conversion
'02 E320 Sdn.(on loan to mom!)
'87 300E (5 spd. conversion) Sold
'05 E500 Wagon