Hey bud,
Sounds like the alarm control module to me. This exact same thing happened to me at Reno last summer. I would fire the car up, and then it would quit immediately. It did this about three times and then nothing after that. It would just crank but it wouldn't fire. It turned out to be the alarm control module, like what Jon B mentioned. The module is just a small plug-in box beneath the steering wheel but it controls a lot of stuff, like the alarm, the door locks, and most importantly, the fuel pump. One tell tale sign is when you stick the key in and turn it to the "on" position do you hear the fuel pump buzzing in the back of the car? If you don't you aren't getting any fuel to the motor and soon you won't even be able to fire the car up.
Did you try to jump start your car in the last three months or so, before putting in a new battery? I did, and I have a feeling I burnt up the module doing it, trying to jump start a Viper can do a lot of damage, but it wasn't until about three months later did the module actually completely go out on me and it stranded me at Hot August Nights.
The module is actually not a hard fix, it is about $200 and it just bungies up under the steering wheel compartment. But if it isn't this it could be your fuel pump going out, which means they have to drop your fuel tank...
