Tore down phone after water damage, still not working?

So I tore down a 4s, down to the display assembly, due to water damage. I cleaned the logic board with 90% alcohol as well as the connectors. There is no longer any corrosion, that I can see. Replaced the battery, and reassembled.

Tried to turn on....nothing. Held down the power and home button and randomly I see an apple logo for a quick second. Sometimes I see a screen that says slide to unlock. Tried to connect to computer and no device is recognized.

Does this mean the display is bad? Is it the logic board? Is it the battery (cheap one of ebay)? Is the phone donzo?

On a side note, after it was dropped in a water, it sat in rice for a few days. It was turned on and supposedly you could hear the clicker and the only thing that didnt work was the display.

How does one go and evaluate what needs to be replaced? I have no problem buying a display assembly to fix the phone, but I don't want to be stuck with it if that does nothing to solve the issue...

someone please help, thanks in advance