How do I know if the battery is dead?

Use this teardown to start your water damage repair.

Then use the Water Damage Guide for how to clean up the phone. Be very careful. The guide really is important because you don't want further corrosion in your phone.

After all that, test out your battery. If it buzzes, but no display, you will need toreplace your front panel assembly. Make sure to swap out the home button, front camera assembly, ear speaker, and heat shield.

If nothing, try a new battery. Unfortunately, anything beyond that and the board may be too damaged to repair.

The links I provided will have links to the tools and parts you need to get everything done.

Good luck and keep us posted.