Does the engine shut off at all after revving to 3K?
And how does it idle in that state? should be around 750 to 900 rpm I think.
I would try and test or have a look at your fuel pump. I'm having similer problems with my 90 525i and I'm replacing the fuel pump. Which will fix my problem. Another thing, when was your fuel filter last changed?
Once the car is warmed up, will it run fine or not?