Runs rough

[Conundrum]

I have a 91 suburban 2wd with a tbi 350 and a 700r4, I bought it in April 08, it takes a little time to start when its cold and has an eratic idle when it is running. For some background on it, it was bought from a local highschool the same day they had put a new crate engine in it (now has around 40,000 mi on it). It has a new alternator, had a transmission installed in Apr of 07 along with a fuel pump (they went out on the same day). The reason I know this is my wife works with the lady that used to own it and she has told her all about it. And she says that it run fine until a local shop put the fuel pump in it, and theey told her the oil pump was bad also. I have noticed that the oil pressure is a little low. I have been trying to figure out why it is hard to start, will die from time to time, and sounds like it has a misfire. a couple of friends of mine and I worked on it for awhile changing the cap and rotor, tried the tps, checked for vacuum leaks, checked the firing order. My question is, would a bad or wrong fuel pump or a weak or bad oil pump cause this problem?

Thanks for any help.