Based on the fact that you had such big power drain already, a board or part issue is quite likely. A replacement battery and dock would be the bare minimum to start troubleshooting but may turn out useless in the end, same as a replacement logic board if you have there a faulty battery or dock. There’s no real best course of action, DIY repairs are a try and error path with mistakes and unnecessary costs involved. Sometimes the best choice is just to have the phone looked up by an indipendent repairer, but if you want to try fixing it yourself either you buy parts or you’re stuck.