As Ken had stated, you DO need to replace your old battery. You can get one
at any Radio Shack or usually any place that sells digital camera batteries.
I've found them at places like Walgreen's, Wal-Mart, etc. In my opinion,
since this is the cheapest option, you should try it first. If that doesn't
work. Your next best bet is replacing your PSU, which you can get at Best
Buy. The power supply is held in place by 4 bolts and the wired connections
going from it into your motherboard. If you need to, you can wrap a piece of
tape around each separate connection describing where it went before. Then
install the new replacement and put the connections in the same place as on
the one before. This works 90 percent of the time. The only other
possibility could be your motherboard(unlikely, but I've seen it), which
could have been affected by a dying power supply. In which case, replacing
the motherboard would be the most expensive and time consuming to replace of
the three. Good luck!