[Android Central Question]

It was wet and I cannot turn it on. I have important information stored there.

[jasonandrews25788]

try to replace the battery maybe its damaged.

[Rukbat]

If the phone was wet, consider it gone. That's what backups are for. (Don't waste your money on a battery.)

If you're a really good technician, and have access to an electronics lab, you could probably extract what's stored in the phone, but otherwise - no, you can't. (You'd have to connect a CPU emulator to the chip to read out the storage portion, or remove the SoC from the motherboard and solder it to a working board - neither of which any real technician would waste his time doing, due to the small chance that it would work.) See Oh, no! My Phone got Wet! in case you get another phone wet. (And back up everything you don't want to lose, from now on. Between Drive, Dropbox and Mega, there's plenty of space.)