1979 Mercedes 450SLC stood in a garage for many years and refusing to run and accelerate!
When it originally broke down a mechanic came and drained the fuel, cleaned out and replaced the fuel pump and filter and got the car running for a short time, but very roughly. It then stopped working again and was left in the garage for a further 10 years.
Another mechanic has visited recently, cleaned the system out, burnt the fuel pump out trying to rev the car and replaced it with a Mercedes pump. The car will start and ticks over, but very roughly and the fuel pump is noisy all the time. Any attempt to accelerate causes it to conk out immediately.
The following helpful suggestion from another forum has been tried but, disappointingly, was not successful
This may just be a stuck air flow plate/ fuel distributor plunger, common fault- the round silver plate in the induction plenum chamber moves up and down under varying loads and pushes a plunger up inside the fuel distributor, remove the dist block from its baseplate- do not dismantle this, just remove the 3 holding screws and turn this over in your hand. You will now see a shiny ball ended plunger that may well have stuck in place, remove gently without burring, clean in solvent and make sure it moves freely in and out. This was the most common cause of idle but no rpm and they would stick after a short time if they had been stood and plunger moved to a new position.
In my opinion (as a humble builder and not a car mechanic) the fuel pump is either struggling to pull fuel from the tank or failing to push it through to the engine. Has anyone please got any ideas on what might or might not be going on or going wrong?

You can't burn out a pump by revving the car. The pump gets the same voltage whether you're idling or are full throttle at max rpm.

There is a simple test for that.

The pump is supposed to deliver at least 1 liter of fuel in 40 seconds at the return fitting from the Fuel distributor (Fuel pressure regulator is built into the distributor on your car).

You do that by having the engine off and jumping the fuel pump relay.

More details on this procedure:
https://www.startekinfo.com/service/download-document/outside/11883/PROGRAM/Engine/107/M117_45/073-130.pdf

When doing this test make sure you take all safety precautions when working with gasoline (fire extinguisher and safety gear) and be away from any expensive things (such as houses)

If it passes this test it will mean that:

-Fuel filter is good
-Fuel pump is good
-No blockage at the tank
-Fuel accumulator is good (At least shouldn't affect running if there's a small leak inside)
-Small filter at the Fuel Distributor is good

How does it look if you take off the oil fill cap when it is running?

__________________
[SIGPIC] Diesel loving autocrossing grandpa Architect. 08 Dodge 3/4 ton with Cummins & six speed; I have had about 35 benzes. I have a 39 Studebaker Coupe Express pickup in which I have had installed a 617 turbo and a five speed manual.[SIGPIC]

..I also have a 427 Cobra replica with an aluminum chassis.

Pictures?
The SLC has got to be one of my favorites.

How's the rust condition on it?