This is assuming that your problem is cranking the motor, not getting the motor to fire. Frequently people will say "my car won't start" - which is too vague to know what is really the problem. If when the key is turned, the motor doesn't rotate (crank), then the car 'won't crank'. When the key is turned if the motor cranks but won't start, then the car 'won't fire'.

I think from your descriptions, the car 'won't crank'.

There are several items that can cause these problems:
Low battery
Starter motor
Starter solenoid

If the battery is low, when you attempt to crank the engine, you exhaust the capacity of the battery. Since a battery makes electricity by chemical reaction, allowing it to sit briefly after this effort can result in enough recovery to permit a start.

Starters that are on their last legs sometimes start the motor fine when cold, but have trouble when hot. You can tell if the starter is "trying" to crank the motor by seeing what happens when you crank the motor with the headlamps on. (Assuming MB doesn't switch off the headlamps when you crank - I've never tried it.) If the lamps start out nice and bright and dim noticeably when cranking, then return to full brightness when the cranking stops, then it's likely the starter.

Starter solenoids that fail usually result in a starter motor that just goes "click" as you turn the key to the crank position. The test above will show no difference in the headlamp brightness if the solenoid is the cause. (No current passing to the starter, so no draw on the battery).

I'd start with a fully charged battery first. Some people have had baaad luck in jump-starting their MB's, so I'd try getting the battery charged first. Most major autoparts stores will test your battery for free - if it's too low to be tested, they'll charge it first and then test it. That will eliminate the battery from the list of possible failures.

Plus, changing a battery on a V12 MB is the same as on a I6 - it's the same battery, and it's in the trunk. Changing the starter is probably a whole other kettle of fish.