W210/E420 Not Charging

[knarf]

Greetings Forum Members,

I'm having an electrical problem with my 1997 E420.
I rarely drive the car, maybe 400 miles per month.
This past Monday I attempted to enter my car using the infared key and nothing happened. I manually opended the passenger's door and soon discovered that nothing was powered in the car. The battery was completely drained and would not take a charge. I purchased a new battery and drove the car latter that day. I checked the alternator output at the battery terminals and it was less than the disconnected battery.
I made service appointment at the dealership for Thursday.
The car was not driven Tuesday.or Wednesday
Today, Thursday, I attempted to enter the car with the infared key to drive it to the dealershipand again nothing. The new battery was completely drained and would not take a charge in 3 days without being driven and no obvious sign of a power drain, i.e lights on device connected.
The car was towed to the dealership.
Has anyone had a simular experience or have an opinion on what the problem might be? I did notice a lingering odor of burning/melting plastic or rubber the last time I drove the car.

Any Help Appreciated,

Knarf