[dr09]

I have a 2007 335i which I bought used last year. Since then I have had tremendous problems with the car. Initially, it was just the long crank, which would only happen occasionally, and usually after it had been cold for 12+ hours, combined with kicking out black exhaust, and a carbon build-up in the engine. It eventually progressed into RPMs when I turned on the car, and rough idling when sitting at a light, and then moved on to a more significant "shuddering" and a service engine light.

Initially, I had thought it was the HPFP, and had it replaced. Now, the service engine light has come on several times spitting out a code that sayis a different cylinder is misfiring each time. I have replaced the misfiring coils in the various cylinders that have errored, and all the spark plugs. However, since then it has spit out a new "Service Engine Soon" light. I have constantly felt like they keep fixing the symptom, without thinking about the underlying cause.

The current hypothesis on the underlying cause is that the fuel injectors are leaking into the engine, causing the it burn off the excess fuel (which leads to the high RPMs and rough idling), as well as the black exhaust.

Does this sound like the right diagnosis? Has anyone had similar issues and had different issues that I might also need to address?

Thanks!