I have a 1995 Chevy Suburban that for years now has a HORRIBLE sputter when accelerating from about 1-30, and lightly sputters as I accelerate to highway speeds (but even then it still does sometimes).
I have recently seen that, as odd as this sounds, it seems as though when I accelerate from 1-20ish it is actually slowing down the harder I push on the gas, so I have to flutter the gas until it gets to a good speed. Idling is fine.

I have a brand new transmission and a brand new air filter, replaced the spark plugs about 2 years ago, and this problem still stands.

I have been reading a lot about bad fuel pumps, but none explain my situation PERFECTLY, and before I get under my car, I want to make sure I have found the problem

Also wanted to point out that this happens about 80% of the time when driving. On the rare occasion, the thing accelerates like a beast (as it should. =P )

Just wondering if this is a fuel pump problem, what I should do, and/or any suggestions.

Thanks!

Oh, and I don't know if this is part of the problem, but when I go to start it, I have to turn the key and it rumbles for about 2 seconds then I let go then turn it again and it starts fine.

 

sounds to me like you have the same problem i have. I have a 99 Burb with TB fuel injection and have basically the same problem but not as bad. I would suggest either rebuilding the carb if its carburated or rebuild/clean the TB unit and go from there if thats not the problem then i would look into the Fuel pump. You can test the fuel Pressure with a guage it should be about 55 psi plus all the time bleed off should not be much if anything at all. If there is bleed off then replace the fuel pump.