"Is it possible to completely wipe the laptop, buy a new battery, then re-install Windows and the relevant drivers to get the laptop back to its original performance?"
Yes, you will need a HP recovery disc set to reinstall Windows.
To possibly solve the overheating see this link
You can order HP recovery media below, or call HP on the phone to order 1-800-474-6836
http://h10025.www1.hp.com/ewfrf/wc/document?docname=bph07143&cc=us&lc=en&dlc=en#N76
If HP no longer has Recovery Media for your model, order them here
http://www.computersurgeons.com/Default.aspx
