The problem may be in your key switch or the sensor that starts it. I've heard there's some kind of reset procedure for the key, but damned if I can find it. Surely one of the guys here that works on them can tell you how to do it. An FSM would be a great thing to have.

 

I don't think the 0443 code would keep your car from cranking- the car would probably run, but the code would stay. That is the emission control purge solenoid code, I believe.
Just to be clear in my own mind-when you get in to crank the car, do the dash lights come on and the accessories work, but it just doesn't turn over? If you try to crank the car with the headlights on, do the headlights go out when you do? If they don't, it means that it is not the battery.
I had a similar problem with my '04 Ion, and it turned out to be grease in the ignition switch(there's actually a sticky in the Forum on this). When mine did this, it threw no codes. You can try to reset the passkey system by turning the key to the start position for 5 seconds, then leaving it in the run position for 10 minutes. Then shut it off and repeat two more times, for a total of 30 minutes. See if the car starts then.
Hope this is helpful.