I have a 96 xj 4.0 that I recieved for free and I cannot get it to run right at all. It has a rough idle and a constant misfire. The engine kinda just chugs around. It currently has no check engine light, but occasionally the TPS sensor would turn it on, but I replaced that, no luck. I have replaced the distributor cap, rotor, plugs, wires, and I even did the head gasket. The oil so far doesn't contain any metal and neither did the filter. Here is a video I took of it starting and running, showcasing what I could.

Things that come to mind.
What kind of TPS did you use?
Mopar or Aftermarket?
The whole really only should use Mopar sensors thing.
I don't see any mention of a fuel filter.
Have you checked your fuel pressure with a gauge?
And last cause I had a buddy go through this with his '96 XJ with a 4.0.
His was running like crap. Did a complete tune up including wires and fuel filter.
Still ran like crap. Drove him nuts.
Finally figured out it was the temp sensor in the thermostat housing.

Welcome to the forum! Time to start troubleshooting!

Since you have a misfire, your rough idle is likely attributable to that. Do you know which cylinder is misfiring? While there are a bunch of things that all must happen in harmony, ignition is actually pretty straightforward. You need air/fuel, compression, and spark.

It sounds like you've verified that you have spark. Now it's time to check fuel and compression.

Start by doing a compression check on all cylinders.

Other cylinders are firing, so you are at least getting fuel to the rail. Perhaps not enough, so check pressure at the rail.

Those are first steps, and will arm you with information to help decide how to proceed.