How do I start my Corolla that has a full tank of gas?

Your fuel pump is shot.....

It got a new fuel pump 2 years ago. Could it be shot already?

Reeelin68 may be right, but there are so many other possibilities. Check for spark, you can do that the old-fashion way by sticking a small/medium phillips screwdriver in a disconnected spark plug wire and hold the shaft of the screwdriver close to the spark plug..or any ground for that matter, and you should have a nice cobalt-blue arc. If you have an arc but yellow, that's a weak spark, but nonetheless and will run the engine. Okay, let's go with you have a spark ....spray a 2 to 3 second shot of starting fluid (You will need a helper) in to the intake manifold, take the air filter out and give her that short squirt of ether starting fluid and if she starts and runs for 5-10 seconds the back to Reelin68 being right in the first place. But as for your question, NO, a fuel pump should not fail inside of 2 years. Or 5 for that matter. This is a 1.6?

Turn the key on. Get underneath it and hit in the center of the gas tank with a rubber mallet. If it starts pumping you need to replace the fuel pump but you will be able to drive it to a garage.

I agree with Fordnut