My touch screen on my phone has stopped working...

I noticed last night that my phone (Samsung Galaxy, just the S1) was playing up and being weird.  This morning, when I turned it on, it loaded up but wouldn't allow me to input my pin number, or in fact, do anything with the touch screen.  I left it on this screen for about 20 minutes (I was doing other things in the apartment) and when I returned, the handset was red hot, so I took the battery out.

 

Now, it won't turn on at all even though the battery is fully charged.

 

What is the best thing to do?  I am reluctant to lose all of the information saved on the phone, and I would prefer a cheaper solution, because I do need a phone that works as soon as possible.

 

Any tips?!