2004 Corolla Won't Stay Running

#1
So, last week I was on my way to work when, about halfway there, my Corolla started hesitating. I'd press the gas pedal and nothing would happen. If I pressed it down far enough (more than halfway), it would seem to "catch" and it would rev up passed 3k RPM's.

I ended up having to pull over. Couldn't get any forward momentum. The car would stay running, but if I give it any gas, especially if only a little bit, it would start rumbling and stall out. I ended up having it towed home.

I've been working on it for about a week and I really don't know what the problem could be. When I start it up now, it may or may not stay running. If it starts, it will idle for maybe 1 or 2 minutes, but then will start rumbling heavily and stall out. It immediately stalls out if I try to give it any gas.

It's not a transmission problem. I can put it in gear and it will move of its own power while idling.

I'd read that typically the fuel filter doesn't plug unless you know there was some type of contaminate in the gas tank. I'm hoping that's the case because I pulled the back seat and attempted to pull the fuel pump, but all of the screws are completely rusted. I can't get a screwdriver into any of them. I'm completely lost. Any help would be greatly appreciated!
 
#2
First of all, you could always buy a screw extraction drill bit to get the screws out. You'll need to buy new screws to replace them once extracted. Secondly, I'm by no means an expert on cars, but, at this point, why not just take it in for service?
 
#3
I finally got it fixed last night. After replacing the fuel filter with no luck, I put a new fuel pump in after drilling out the screws and re-tapping the holes. It’s running great now. It must have been dying slowly over time because it's noticeably more responsive when I press the gas.
 
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