A little help needed, please!

[Madmax]

Hello, I have a 2004 Aveo LS hatch, and was doing some work to it the other night, drained the battery and needed to jump start it. It had a CEL on prior, but I did not know the codes stored. I pulled them today and have c1204, c1201, p01035, p01028 p02610. Im the original owner and the car has 59,500 miles on it. I’ve googled the codes. Do I really have a faulty ECM, or is that just because I drained the battery? I can see the o2 sensor and thermostat, but the other major codes are throwing me for a loop. Any and all help would be greatly appreciated.
Thank you.

[avguy]

First have the battery tested in order to make sure it doesn't need to be replaced. Next replace the O2 sensor and diagnose/repair the coolant temp issue. After all of that, check to see if and codes remain and how it's running.