I checked my spark plugs and have a spark going to each plug. I changed the fuel pump thinking I didn't have enough fuel pressure. I sprayed some starter fluid in the intake and it started for about 5 seconds. I checked all of the fuses inside the car and out. My spark plug cables are new. I verified that both coils are sending a spark. What am I not seeing?

Do real fuel pressure test using test gauge. You changed ignition module but not coil? Are you getting nice fat blue spark? When spraying starter fluid into intake it only tries to start which makes me think you have ignition problem.

Check all fuses first, then with an assistant, check for spark with a spark tester. if there is spark at 2 plugs, check for fuel pressure at the fuel rail with a gauge. Engines need three things to run, fuel, spark, and compression. If there is spark and fuel, do a compression test, if the timing belt jumped/broke, you won't have any

Check your fuel filter. If it has not been changed for awhile, it may be plugged. The car would then be starved for fuel and quit. After sitting for awhile, enough fuel may get through, but after running a short time it will die again for lack of fuel.
Another thing to check is your ability to get spark to the spark plugs. You coil(s) may have died and need to be replaced.
You could also have a crack in your distributor cap if you have one and the spark is shorting to ground. You may also have faulty spark plug wires that need to be replaced. You could also have a blown fuse to feeds battery power to the spark coil. You could also have an open ballast resistor in line with your spark coil and it needs to be replaced. Gas or Spark, but how the spark is generated really depends a lot on the car. Here's a test you can run to check for whether your car is starved for gas: Get a can of starter fuel and spray a couple of puffs (small amount) into your air cleaner. Once the battery is charged, try starting it. If it starts running and then dies, you can be pretty sure you have a gas problem.
One last possibility is that your exhaust is totally plugged. Do you feel or can an assistant feel any puffs or unburned exhaust coming out of the tail pipe? If no vapors come out, it could be plugged.
Oh, one other thing it could be. Your plugs may be flooded, especially if you pumped the gas pedal and it is a new model car. If it smells strongly of gas, your spark plugs may be wet (flooded) with gas. In that case, remove all spark plugs, disconnect your spark system, turn the engine over to blow out excess fuel, dry your spark plugs and reinstall them.

Check ignition and gas.

Listen for the fuel pump to come on for a couple of seconds with key ON. If you hear it, pump is working, check for gas at the fuel rail on top of engine. Should have gas under pressure.
If pump doesn't come on, check the fuel pump fuse, check fuel pump relay. Last, use a test light or voltmeter and check if the fuel pump wire has power to the gas tank connector when the engine is cranked over. If power there, fuel pump will need taken out and replaced. If no power at the pump, pump circuit needs checked.

Check ignition by checking for spark at a plug wire end. Pull off plug wire from spark plug, push the boot back so metal end terminal is exposed. Hold the end terminal 1/4 inch from a grounding source like a metal bracket or bolt on engine. Have a helper crank the engine over and watch for a spark-you need to see a blue snapping spark to know the ignition is good. Maybe wear gloves or use a heavy rag holding the wire-you can get shocked if not held close to a ground. Another way is to pull off the wire from plug, remove plug from engine, then re-attach plug to plug wire, and lay the plug on top of engine where the plug threads are touching metal-now the plug is grounded. You will not have to hold the wire. Have the helper crank the engine, while you watch for spark at the spark plug end. If you have a blue snapping spark, ignition is good. It is a good idea to check for spark on more than one plug wire-maybe another coil is not firing.
If your ignition is good, and you hear the pump come on, possibly a weak pump not putting out enough pressure- then check fuel pressure with a fuel pressure gauge. Fuel injection requires high pressure, so the injectors will spray fuel out.
If still no go, scan computer for trouble codes. Check if your security or theft deterrent has immobilized the car.
Good luck.

I think you are making some assumptions and may be overlooking the problem.
What is the actual fuel pressure at the rail ?
Are you getting a good spark at the plugs ?
Do you have normal compression on all cylinders ?
Is the check engine light on when you turn the key on ?

Could be a relay or other electrical issue.
You say it has fuel pressure and spark, if that were true it should run.
So it either does not have enough spark to fire the plugs under compression, or not enough fuel pressure going thru the injectors, or not at the right time.
You might want to check for trouble codes in the computer.
There has to be something missing from the equation when it won't start. You may have to check all of the plugs for fire and try some carb cleaner sprayed into the intake to boost fuel supply to find the issue.

Are the plugs wet with fuel?
Check for spark. No spark? it may be the ignition module.

Plugs dry and spark present? No fuel?Spray a little starting fluid and see if it will run on that.
Then check pump fuses and for fuel pump noise.

maye it wasnt the fuel pump it probaly was the fuel filter

Sounds like a fuel pump,maybe ignition coil,but more likely fuel pump.Check 1 or 2 plugs to see if you have spark since that's easy enough to at least verify.Pull the plug,plug the wire back on to the spark plug,hold the little plate of the spark end up against the engine block,and turn over real quick.If you don't see anything first time,try once or twice more.Try another plug.If they both spark...you have spark lol.That leaves fuel and air.Even with a serious air problem,it should start and is not likely to just quit.Fuel pump probably is difficult.I have a 1995 and it is under the back seat as a cap on top of the tank :( Pulling off the seat was easy.There is a lock ring on the cap/pump that was slightly rusty,enough so that I had to buy a used tank and a new pump.If you want more specific location of your fuel pump,call the dealer or a shop.Someone will usually give you free advice to attract future business.
Good luck! Greg

Here is a pic of a schrader valve. They all look about the same.
If there isn't much pressure, cycle the ignition without turning the engine over and try again. If it is still weak, you may need a new fuel filter. If it is strong, you may have dirty or clogged fuel injectors.

It may be spark, but I'm inclined to think it is fuel related.

Good luck, and keep us in the loop!
JT