00' SL2 Tempermental starting.

I first had a sign of a problem about two weeks ago. Went to a restaraunt for breakfast and came back out about an hour later and started the car. It sputtered at a rediculously low RPM (So low that the idiot lights were still on and it didn't seem like the computer registered that the engine was even running.) And stayed idling like that until tapping the accelerator which brought the idle up to normal. It has been pretty cold here, but its never ever given me problems starting in cold weather. And a few nights ago it wouldn't fire up at all. The next morning when jumping it had to hold the accelerator about half way down to get the engine to fire up.

I had done a semi-quasi tune-up on it about 20,000 miles ago on it, but didn't have the money for a fuel filter. (They are a rare beast and therefore expensive.) Could this be the problem? Or does anyone have suggestions?

Replace your engine coolant temperature sensor. I posted a video in one of the last 5 threads.

Replace your engine coolant temperature sensor. I posted a video in one of the last 5 threads.
Wouldn't the check engine light come on if a sensor was bad?

One would think, but no. This sensor is vital to all subsystems of the car, the most common sensor to go bad, but will not set off the SES light.

10 Bucks at autozone.

could also be a dirty throttle body or bad TPS or idle air control valve.