You say you put a new battery in, but you are describing the symptoms of a bad battery.

Start the engine, then use a digital meter and measure the battery voltage - is it above 13.8 volts? If not, the alternator is not charging and you can get symptoms like you describe.
The p0600 is simply telling you the same thing all those lights are telling you - the CAN BUS is compromised and modules are not talking to one another like they should. I doubt you have a bad module anywhere, altho is it possible one failed if there were a lot of swings in system voltage as the battery and\or alternator were dying.

My seat belt module was destroyed when my battery failed. This is why I usually replace batteries at 48 months, but I'd just bought the car and had not looked at how old the battery was. In any event, do not be too quick to assume you have a dead or damaged module, let's make sure the battery/alternator combo is OK first.

It is WINTER, if this car has been driven in the U.P. of Michigan a lot in the past, I'd do the "ground to the block mod" NOW, TODAY, before you do ANYTHING else.
See this link, do either James' or my mod - do this FIRST then let's move on from there.
Click this red text for your first mod!