My iphone won't turn on. Is it completely dead?

My iphone 4s was getting really hot when i used it for a longer period.
one morning when i woke up it was really hot and didn't turn on. I let it cool down and then i kept trying to open it but it didn't work. I also tried to hard reset it (home+lock button). Nothing happened. Yesterday i replaced it's battery with a new one. Still doesn't open. What can i do? I have a lot of data in it that was not backed up and i need it. Can i fix it?

I can tell the problem from your description. I think the only way is to send your phone to a repair store.