can't restore iPhone 4S with backup/Phone restarts itself/Bottom row of touch screen does not work

Right, so I did this stupid thing where I dropped my iPhone in water a few days ago. Stupid, we all know that, but that happens.

Now I have two problems/questions. I got it out of the water immediately and got rid of all the water on the outside, now the problem was that it did not turn itself off (it resets whenever I do that), it still worked perfectly fine. I put it in a bag of rice of more than 48 hours and let the battery just drain out.

Now the bottom row of my iPhone does not work, I can unlock it and I can unlock my sim card, I just can't use the very bottom row in every app and on the homescreen. I've just tried to reset and restore my phone but that gave me a second problem: I can't reinstall my backup because my phone does not restart.

Now my questions are:

1. If I restore my phone as 'new', do I keep my old backup on itunes? Or is there any way I can keep the backup? If not, should I leave it like this, try and get it fixed and then restore it with my old backup?

2. What could possibly be the problem with the fact that my iphone doesn't shut down?

3. What could possibly be the problem that the bottom row does not respond? I'm guessing I'll just need a new digitizer or something along those lines.

I don't have warranty or insurance on my phone so going to the apple store is not really an option. I know someone who can fix the screen for cheap, I just need to find a solution for the backup problem, I don't fancy losing everything I have on my phone.

Thanks in advance.