My E36 had the carbon build up problem, about as bad as you could imagine. 25 years of New Jersey 87.

It was consistently the same throughout the entire rev range, nothing unusual off the line. It was just bogged down and tired through the entire rev range. You give it full throttle and it didn't want to do it.

I ran a few cans of berryman b12 through the fuel and the crankcase, that helped a little bit. I used the liqui Moly engine flush twice, that helped a little more. A lot of people say not to use that as it can dislodge something etc but I've used it a bunch in all my cars and been lucky. It does help. But I still had to take the head off and clean it by hand. It's normally responsive now, but I did about 60 other things in addition to the carbon cleaning.

I don't think carbon is your problem.

My f30 does all this kind of crap, it's the computer. The dsc, and the e differential, torque , limiter, dual mass flywheel protection nonsense. Some of this can be coded out but it's an uphill battle on that car. Sometimes off the line I'll get exactly what you describe, and then into second it cuts out. Then there's shadow codes for flywheel protection.

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'05 E53 3.0 6mt
'17 F30 340ix 6mt
'93 318is, zf5 m52b28 swap