First of all:

1. If the car shuts down with the key in the "2" (start position) then you must completely turn the key to the "0" (key release) position before attempting to start again. When you try without going all the way back to "0", then you will get only idiot lights like you describe.

2. The real question is why is your engine just shutting off by itself. If your cranking problem is related to #1 above, then I believe it would be the CPS. It's a cheap part and very easy to replace.