2008 Dodge Magnum check engine light and codes

So one day it was driving fine. Made a stop to shop when I came out and
started the car the check engine light came on and was running rough.
I let it sit for a couple of days and the battery was dead. Discounted the
battery and charged it. Connected the battery and car ran fine. Drove it for a
little while and shout it off. Again when I started it the check engine light
came and was running rough. Had codes 0301, 0204 so I replaced all the
plugs and coil 1&4 connected the battery and started fine again when it got
warn the codes came back. Then got a code of 0300. So I did more research
and found it might be the battery. So I bought a new one and the cars check
engine light was off and no codes. It ran fine for 3 days. Starting and
restarting. Then it happen again. So I change the alternator  ran fine till the
check engine light came on again but went off. Made a stop and got back in
the car and again the check engine light came on and the car was running
rough and a code of 0301. So how can it run fine sometimes and go bad
after shut off??????