hello my dear corolla members...
Long story short: Friday night I was getting ready to go to the store and pick up some food, hit the remote start button to warm up the car for a few minutes... after I went outside the car was not running??? Tried to start the car with the key, the car turned over a few times but could not start battery was weak and it was really cold outside close to 0... Jumped in my other car no problem there... The next day I tried to started it again no luck the battery was dead.
Today I got a new battery, the old one had sticker on it from back in 2005...
Put the new battery, went inside to start the car NOTHING the engine turns over like crazy but it will not fire????

I can't really hear the fuel pump (could be a bad pump???)
Is there something else that I need to check before I assume that I am dealing with a bad fuel pump???
the car is 98, 215,XXX miles, new plugs about 17,000 miles ago...
Prior to that the car was running kind of weird, it still had plenty of power but I could tell that it was not like before... and also the MPG went down a little...
Is there something like ignition switch/coil or something is this area that could cause the engine not to start???
Thanks!
Update: just checked with the OBD scanner no codes (probably b/c the battery was disconnected for good 2 hours)