Coil and cylinder firing order

Maybe this diagram will help you. The engine block of course is the big one and the small one is your coil

I installed a new # 4, 1 coil and there seems to be no change. The car seems like it wants to shut off when pulling off. It is like after it catches or something, it starts moving. After it warms up a bit, it seems to run better. This vehicle was sitting for two years or so, and there were never any maintenance done to it after the second owner got it. It has over 211k miles, and I do not know what else to do. After it runs a while, it runs pretty good. it is the initial start off when I first crank it up. I ran the old gas out of it, dropped a bottle of LUCAS in the tank, and a can of restore in the oil. I am hoping that it will help. What do you think.

If no maintenance been done to it, changing spark plugs and especially that fuel filter would help alot

I changed plugs, wires, oil, and coil. Have to change oil again because what I thought was oil filter ended up being the transmission filter. The only issue I am having is the loss of power when I first pull off. I haven't gotten it inspected yet, and need to put it on the highway and blow it out. Trying to get it through inspection. Check engine light keeps coming on. I am really puzzled.

What codes are in the pcm?

haven't checked yet. The last was showing misfire in cylinder #4, and random misfire in others.??

Ok make sure you check even the pending codes, and an intake fuel flush wouldn't hurt. It will help get all that carbon build up out

The codes I am getting is P-something 300 and 304. Say #4 cylinder misfire and random misfire. Cleared the "service the engine soon" light and it came back on. Haven't really driven the vehicle but planning to drive it about 60 miles or so on the highway later this evening. What do you think?

3 rhings, make sure you got the wires going to the right coil spots, check compression on the cylinders especially number 4, check to see if you getting power to the injector number 4 with a test noid. I wouldn't drive it a lot if it's missing

how do I do all of that?

The diagram i sent earlier go by that to make sure the wires are located in the right spot. The rest you need special tools like compression gage, and some noid testers to,check power for injectors

I am getting the following codes:
PO 507
PO 300
PO 171
PO 304
I changed plugs, wires, and coil for cylinder 4 and 1
Changed oil and filter, changed trans fluid. Car is running much better with no power loss. Do not have air filter yet, and can barely hear a slight miss. Still getting these codes. Wondering if missing air filter has a lot to do with it. Trying to get it inspected. Running out of time and money. What are your suggestions?

Sounds like you have a vacum leak somewhere. Make sure you don't get dirt in your mass air flow sensor since you have no air filter in it. Get air filter and check for vacum leaks make sure your throttle body is clean aswell