Iphone 5 to 4 with sim card?

I have an IPhone 5C, and recently dropped it, and now it won't turn back on (and yes I have tried to charge it). So I have decided to just use my old Iphone 4, but it does not have a sim card slot. How do I get my info back? Can I put the sim card into my mom's Iphone c, put it on the computer, and then put it on to the 4?

Yes

Who is your telephone provider? If they have an office/store nearby, they can help you with that. Take it to them.