"" Died, due to a dead battery (cable problem - replaced) ""

Did the wire leading from the alternator fail and battery stopped charging?

Even a battery that would barely crank a lawn tractor won't cause the car to stop once running if the alternator is working so the stoppage might be from another source.

Was it a large cable that leads directly to the battery that failed? How did it fail, broken wire , corroded completely through, insulation falling off and touching ground?

If this was the smaller wire on the positive terminal that feeds the body, you may still have a break.

On a 98 and up W210, if the key fob turns, the fob is OK. These use an electronic steering column lock not a mechanical key. When you insert the fob, you will hear a ZIP sound of the column unlocking.

I don't think the dealer can program a FOB for electronic lock even if they wanted to, you need a bootleg China programmer for that. But, if the key turns you problem isn't there.

Do you have access to an OBD2 reader? You need to see if the engine computer is waking up.