Water damaged iPhone 5c. Have I fried my battery?

So I dropped my iPhone in water a few days ago. When I took it out, it was still responsive for a second or two, but then it blacked out. So I have had it in rice for the past three days. I plugged it up to a charger this morning, and the little "You need to charge your battery" symbol came on for a few seconds, and then the Apple logo appeared (which generally means the phone is turning on). However, after a few seconds the Apple logo then also disappeared, and the low battery signal came back on. It keeps alternating between those two symbols, but if it's not connected to a power source it won't come on at all. I'm assuming this means that the battery is dead, because I've tried a hard reset and everything else, and it's not responsive. So is it indeed the battery? And if so, do you think it would be worth trying to replace it considering the possible water damage? If not, I'll just pay the $200 deductible and get a new one. But I'd like to at least try to salvage this one.

Thing is with liquid damage you don't know what may of happened. And I know Apple will charge you a large sum of money to get a replacement due to damage.