And you didn't immediately turn right around and go back to the mechanic to have him fix it correctly why? Is it correct to say that the engine wasn't running this way before the fuel pump was replaced (back when the old one was working)?
When you unplug the MAF sensor, it puts the system into open loop mode, running off the computers presets instead of all the sensors. I suspect it may be a faulty sensor, other than the MAF, giving a bad reading when in closed loop mode. From what you describe, it sounds like the engine isn't acting up when it's a cold start?

 

Basically, I'm tight on money after dropping nearly $800 for the fuel pump and labor, so I figured I'd leave pricey mechanics out of this equation. Are there any ways (other than checking voltage) to check if the MAP, o2s, IAC are faulty? You're right Camaro69, it starts up perfectly fine on a cold start.

 

I think you missed my point about the mechanic. If the engine was running fine when the other fuel pump was still working, and now it's not with the new pump, the car shouldn't have left the mechanics place with it running bad like that. Maybe he bumped, knocked, or broke a sensor or wire when he was under the hood checking your fuel pressure. Never know.
Let's start with what most likely is not the problem:
MAF sensor - you replaced with no difference
MAF circuit - unplugging the MAF makes a difference = connection
When in open loop (your cold engine, or when you disconnected the MAF) the computer makes the engine run with a richer air/fuel mix than when it's in closed loop and running off all the sensors.
So it sounds as though your engine is running lean when it goes into closed loop mode.
You're getting a random misfire code. Here's a list of possible causes of a random misfire: non-working or clogged fuel injector(s), bad spark plugs or wires, bad coil pack, bad/restricted catalytic converter, bad oxygen sensor(s), stuck or clogged EGR valve, faulty camshaft position sensor, burned exhaust valve, defective computer.
Now a couple of those things (cat, EGR) can get pretty much ruled out, as they would make the engine run bad with or without the MAF plugged in. And I would expect a cylinder specific (not random) code if things like the coil or cam pos. sensor was bad.
My first "guess" would be to check the fuel injectors, either not firing or not flowing well. Then the spark plugs and wires. Those last two are a possibility, even with the changing MAF, since a plug can have an easier time firing with more fuel than less (your open loop rich condition). Oops.....this response got a little long!!

 

Thanks! I'll get on that today. I appreciate the responses

 

Fuel injected cars run in two modes: open loop and closed loop. when an engine is cold or the trouble lamp is lit, it operates in open loop and most sensors are ignored. When the engine is warm and the trouble lamp is off, the engine operates in closed loop and all sensor inputs are observed. By you unplugging the MAF, you forced the engine to work in open loop and follow a preset program. The fact that the engine worked better with the MAF unplugged indicates that one or more sensors are bad, but not necessarily the MAF. You need a scanner to look for trouble codes, if no codes are set or retained, you need to use the scanner to look at the output of each sensor and see if it makes sense for the conditions at that point.

 

Turned out that both MAF sensors I used, (the old one) and (the new one) were both faulty. I obtained another new MAF sensor and plugged it in. My car runs like new! THanks everyone for the helpful info.

 

Sheesh! Was the new one "new", or used but new to your car? If new, I'd avoid that brand again.

 

It was brand new. Autozone had it and it was the cheapest one at just under $134...needless to say I got my money back from that one and put an extra bit of cash in for the more expensive one.