We have a 88 300SEL that was my car, now my moms... it did the SAME thing! I drove it to a gas station back in July - it was running perfectly, filled it up, then it would not start at all. We had to have it towed home. Next day the car was trying to start (see video below) and following days we were finally able to start it, but it would miss, sputter and stall on acceleration. One day we started it... it idled for 15 minutes just fine, but when we would press the gas, it would stall or start to miss and splutter. We checked the fuel pump relay (bypassed), that wasnt it. Checked this and that - was told it cold also be the fuel pump or fuel filter. Finally someone told my dad to check the ignition coil. He took one off of my 72 Chevy wagon and used it long enough to see if you can believe that and sure enough, it ran perfectly. $105 later for a correct coil for the car and it has ran perfectly ever since. We also did replace the rotor button I think and I replaced the spark plugs after that.

Not sure if this is your issue or not, but just wanting to relay what the issue was on our 300SEL.

Here is a video I had a neighbor do back when it was having the issue since my camera battery was dead. He has a W126 and had been helping me w/it. This was back when it would only try to start... we had finally got it going after this, but it still would miss, sputter, etc.

Click on pic for the 2 minute video.... see if this is how yours is doing.