I need help with my laptop?

I bought an HP G60 about 3 years ago & I am having major problems with it. I have had to replace the screen because it overheated & the screen cracked. I have to have my laptop propped up on something sitting on a table or something so it won't overheat. It gets soo hot it burns my legs and the charger sometimes says it isn't charging & other times it does charge. When I have it on for a few minutes it beeps once it's never done that before. Also when I shut it down it takes it a few minutes and the screen will go black before my computer shuts down all the way and I can't restart it anymore because it won't go off and come back on. It isn't under warranty anymore or anything. Is there anything I can do 2 fix any of this at all. Thank you.