Hi Calion,
The problem is, water (liquid) damage is always a crapshoot. Ideally you'd want to open up the phone and clean everything you can with high purity isopropyl alcohol. That kind of repair needs to be done as soon as possible after the exposure to minimize corrosion and circuit damage.
I'm skeptical that replacing the screen will help. The fact that you saw the Apple logo indicates that the screen is still functional and that it's something else that's keeping it from booting.
If you're comfortable with doing your own repairs, take a look at these guides to liquid damage on iPhones.
[guide|5825|Repairing iPhone Liquid Damage - iFixit Repair Guide|new_window=true]
[guide|95280|iPhone Liquid Damage Repair - iFixit Repair Guide|new_window=true]
If this looks like more than you're comfortable with, then I'd suggest taking it to a repair facility that's experienced with liquid damage. But whatever you decide, you definitely want to do it sooner than later. The longer you wait the worse the damage can get.
Best of luck with it, and let us know how it goes.