Will verizon fix a problem on a phone not related to physical damage that it has?

I have a droid 2 global and the screen is cracked. I don't care that it is cracked and that is not bugging me. It has other issues that are though. Whenever I charge the phone it gets really hot until I have to unplug it and pull the battery and let it cool down. The phone freezes all the time and will become unresponsive. It also restarts it self if it freezes enough. I know the screen is cracked but will Verizon fix the other issues? Thank you.