I'm moving your thread to the laptop forum, but quite frankly, I think you would be much better off investing in a new laptop. You can get a brand new Dell for a $400 base price.
There are many things that could be wrong, including a bad motherboard, or a bad power supply. So you could go to the expense of replacing parts one at at time without a real clue as to the extent of the problems, or you could simply get a good working laptop as a replacement.
The chipset refers to the entire integrated circuits of the motherboard, and traditionally includes both a northbridge and southbridge, though many modern designs don't have this separation anymore. http://en.wikipedia.org/wiki/Chipset