switch displays

Yes, it should be completely possible.

http://www.ifixit.com/Browse/MacBook

You'll find detailed step-by-step guides on doing pretty much anything to your MacBook there. Good luck!

 

alternatively, get yourself an external monitor on the cheap and hook it into the macbook. no repair involved. replacing an LCD panel on an original macbook is a somewhat difficult process if you are not familiar with it.

You will need:
External monitor
DVI-miniDVI or VGA-miniDVI adapter, depending on the display

Hook the display in and press Fn+F1 (or Fn+F7, I forget) on the macbook and voila, macbook on your external display

 

Yes, this should be completely possible, so long as they in fact are the same computer. Also as the guy below said, you should be able to use it with an external monitor if you'd prefer to not go through that hassle, and are not very mobile. However, you might want to see what is wrong with your older computer and possibly fix it and just use it as a desk top with an external monitor