How to Troubleshoot More Complex iPhone Problems?

So, here's the background on my problem.

Dropped phone in salt water.

Did NOT try to turn it back on.

Took apart, cleaned to avoid corrosion and dried it.

After a few days, put back together.

Blank screen, iTunes recognized it but would error when restoring.

iTunes Stopped recognizing.

Installed new battery and dock connector.

Phone was charging but would not be recognized. I say it was charging only because the battery was getting a little bit warm, so power had to be going into it.

Now it's not doing anything at all, no warmth coming from the battery and the computer will not recognize it. I've tried multiple cables and usb ports on two computers.

I may have put a screw back in the wrong spot and damaged the mother board but I honestly don't know. I've tried everything I could think of and most of the phone repair places near me only do simple stuff like screen replacement.

1.) How can I go about troubleshooting this problem?

2.) Is it possible to restore an iphone without the screen cables hooked up? I ask because I can determine if it's a screen problem as well as something else.