That sounds a LOT like the fuel pressure regulator issue I had. The fuel pump delivers a constant fuel pressure that is more than the injectors need, and the FPR regulates how much pressure is in the fuel lines at the injectors (open for less pressure, closed for more pressure). When the part fails, it gets stuck open. When this happens and you shut the engine off, the fuel is allowed to drain back into the fuel tank, leaving the lines dry when you go to crank the next time. When you turn the key to On before cranking, it gives the fuel pump a moment to prime the lines.
This was the issue on my 01, and I'm pretty sure the system works the same in your year. The dead simple way to check for whether the FPR is the issue or not is to pull the vacuum hose that's connected to it and smell it. If you get a strong fuel smell, it's bad. A faulty unit will allow fuel into the vacuum lines.
The other common culprits are your injectors leaking or the check valve in the fuel pump failing. If your injectors are leaking, you'll get things like a lot of smoke on startup and possibly a flooded engine. The only way to absolutely verify that it's leaky injectors is to pull the fuel rail, prime the system, and see if they leak. If the check valve is failing, you'll have the same symptoms as a failed FPR. If the check valve is faulty, however, you'll need to replace the entire pump. Fortunately this isn't quite as common.
The other troubleshooting step to try is to get a fuel gauge and hook it to the fuel lines near the fuel rail and watch what happens to the pressure when you shut it off. A healthy system will maintain some pressure for at least a few minutes, and maintain a small pressure over extended periods of time. Mine was going straight to zero. The FSM gives more detail on what tool and where exactly to hook it up. I'm not sure where it is, exactly, since you have a different year than me, but it'll be in the fuel section.
The part was about $70 and super easy to swap, but your mileage may vary
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Consider changing your oil and spark plugs when it's fixed too. A bad FPR probably means the engine is running rich, and an engine running rich is likely to wash the cylinder walls. That means gas hangs on the walls and ends up in the oil. Fuel breaks oil down, which is bad for obvious reasons. The spark plugs are also likely contaminated with soot and such.
If you end up replacing the FPR, consider replacing the fuel dampener as well. It's about the same price and not too hard to replace either. It helps with smoother fuel delivery. Definitely not a must, but food for thought.
Sorry for the lengthy post. Let me know if you have any questions, and good luck!
