You've probably reached a point of diminished returns as far as reapiring this phone.
Water damage outside of a warranty claim is usually a case of throwing good money after bad.
You could go to just about any cell phone provider/retailer & request that they allow you to troubleshoot w/a battery that they may have on-hand.
However,this probably isn't the issue,since the phone powers up,the battery is working.
Sorry that I don't have a better outlook for your situation.
The only other possible solution is to power down your device,remove the cover & battery & leave it unpowered for a few more days.
It might dry out enough to salvage,but,since the phone has already been powered on & damage has been noted,the odds of this clearing up are minimal.
Best of luck to you & please feel free to drop back by & give us an updateon your situation.