You definitely need a bigger power supply.
If you bought your machine from a name brand maker, for example Dell or HP,
you have to make sure that the motherboard can accept generic power supplies
without frying itself. I have yet to see a machine from a big box store that
had an adequate power supply in terms of wattage or quality.
Rather than replace the power supply consider putting one of your hard
drives in an external enclosure. That way it will have its own power supply
and you will not have to replace anything inside your computer.