@"oldtimer 11"
When you turn the key on the fuel pump only runs for a second or two and then shuts off.
To remove the gas from the tank, it’s easier to remove the fuel pump relay and insert a jumper wire into the relay socket so the fuel pump runs continuously.
Tester
You replaced the cat, but what about the rest of the exhaust system. My first inclination was an exhaust restriction. Second is limited fuel delivery due to a clogged filter or bad fuel pump.
Timing could be an issue. The timing chain gets oiled when the engine runs. When it sits up for 5 years, the chain can rust in position. When you try to start it, the parts of the chain that went over the gears does not want to straighten out and the straight sections do not want to go over the gears.
I don’t think there is enough play in the gears to skip a tooth, but they could shear off the woodruff key in one of the gears allowing it to shift on the cam or crankshaft. The material of the woodruff key and the bolt holding the gear may limit its slip to a few degrees, but it could be enough to cause the valve timing and the ignition timing to be off enough to cause these problems.
I only replaced the cat converters with a big Y-pipe assembly piece l found on rockauto, l didn’t think to inspect the rest of the fuel system before doing so…l hope l haven’t already damaged the new converters…
Can bad timing cause major compression loss? As ok4450 said, the compression is pretty bad.
Should l keep trying to pinpoint the issues and fix them individually, or just go all in and get a remanufactured engine from the ford dealer?
I got a quote today for a remanufactured long block + labor for just over $4000. Cost isn’t really an issue in regard to quality, assuming l’ll be getting what l paid for…but is $4150 too much? Too low? Fair?
Better yet, should l focus on the fuel and exhaust systems before getting the new engine? I don’t want to end up kicking myself in the head for ruining a brand new engine. Heck by the end of all this, l’m gonna have a brand new car! 
yes, buy a 15 dollar fuel filter first. as you said earlier you should have
oh, don t ever tell a mechanic , or anyone, that money is no object.
Bad valve timing, which you would have if one of the pulleys slipped out of position, would cause low compression. I don’t know if you engine has timing marks anymore, but if the valve timing has slipped, the ignition timing would also.
Your compression is on the low side, but I don’t think that alone would cause this symptom. Compression in the 110 range would more likely show up as a slower 0-60 time, say with the correct compression you’d get 10 seconds, with the lower compression you might get 13 seconds. That’s assuming all the cylinders are basically working, just a little low on the compression.
The symptom seems to me more something is partially clogged up between the air intake, the fuel system, and the exhaust. Fuel filter, muffler, fuel pump, fuel pressure regulator, air intake, air filter, something like that. You might just have a bunch of acorns in the air intake deposited there by rodents, so get out a flashlight and take a close look in that area.
The advice above to have an accurate compression and vacuum test done is spot on. And to of course make sure all the routine engine maintenance suggested in the owners manual is up to date.
there is a motor in there? car sitting for yrs? grungy fuel pump pickup? bad fuel pump?
Thanks for the correction tester. I thought it ran until it built pressure.
@Torinosuke – Reading this thread has me thinking you are asking too many people and too many places for advice. Firestone is for tires and basic repair. At 19 years old I would hope you have someone in your family to help you. At the rate you going you will have entirely too much money in an old car . The person helping you does not need a lot of mechanical knowledge just be a sounding board so you don’t waste your money.
Good advice Volvo, but I would have omitted basic repair. I once emptied out a Firestone showroom by telling at one of my sons who had taken his car to them for inspection. They failed him on the inspection and gave him a laundry list of repairs that far exceeded the value of the car.
What I was screaming at him was. “Didn’t I tell you never to bring a car here for anything but tires”.
In case you are wondering, that Firestone store did have a showroom, the building had been a J C Penny’s Auto Center in the days when they tried to compete with Sears on every front.
Pull the vacuum line off of the fuel pressure regulator, if there’s gas in it the diaphragm has broken and gas is getting into the vacuum of the intake. Replace regulator.