Serious Problems
 

Ok I have an 01 Grand Marquis, but I recently had a 2000 engine put in it to replace the old one and when they put this engine in they had cut wires on the old spark plug and fuel injector harness and switch them with the other plugs.

Now I don't know whether that's the problem or not, but my car is having some serious problems. When I press the gas it kind of jus slowly moves just bumps slowly before finally getting some power to move and when I press the gas when i'm driving it starts doing the same bumping movement and you can hear the problem building up as I have the gas pressed down until it finally comes back, if I press the pedal all the way down it'll actually do it without that much bumping.

I don't know whether it's the wiring, the spark plugs, the fuel injectors, or the muffler, because you can hear a noise coming from the muffler sounding like it's barely puffing air out the muffler kind of like a constant cough. Can anyone help me with this

sounds like whoever did the engine swap for you screwed you over. check the firing order to make sure it's ok and you'll probably need to double check ALL the wires going to the engine to make sure they are not disconnected somewhere.

I can't believe they cut the wires instead of properly disconnecting stuff (adds a little to labor in the swap, but saves tons of headaches later).

X2 on what Slymer said.. Although I would imagine laborwise it probably would have just been easier to unplug and swap the harness.. None of it is that hard to access...

A few questions though,
Has it done this since the new engine was installed? And is your check engine light on? Does this "bumping" sort of resemble a backfire?

It wasn't really doing it that bad at first. Yes the check engine light is on and it kind feels like it's going to back fire because while the engine is building up you can hear a noise coming from the tail pipe as if air is kind of coughing out and not coming straight out. I'm starting to feel as if it's in the exhaust because after driving it for a while you can start to smell something like really hot metal or some kind of smell and you can start to feel a little heat coming from the floor.

The cat could be clogged which would account for the exhaust note, lack of power and smell (rotten eggs?). But I agree with Slymer and Max and say there is much more wrong here and the swap was muffed in a bad way. Are you sure you got a replacement engine with no previous probs?