A little help needed, please!

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.

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.