2000 Neon Engine Codes

I'm getting (P1684) I think it's the battery disconnect code, and (P0442) that I think is the evapurative system code. My kids have left the gas cap loose once before on this car and the dealer just got rid of the check engine light. The car has more than 36k miles on it now and I'm wondering if anyone knows if this light will go out on its own?

Disconnecting the battery for 10 seconds will reboot the engine controller and reset the check engine light. This is probably what set the first code. The light will reset itself after 50 key starts if the condition that set the code is no longer present or another code has developed. The Evap purge code may indicate further problems.
Try the battery disconnect method first and see if that's all it takes.
RG