lehtv is right, there's no real reason to replace the PSU if your computer is working fine.
Core 2 Duo e4600 is still decently fast, so the system has plenty of life left.
The only concern is that I've seen no-name brand PSU take out motherboards when they die.
If you'd like to continue using it, I'd invest in a low cost PSU from a name brand (antec, corsair, seasonic) with atleast 300w, particularly if its on sale. Cooler Master and other brands also have good products, just make sure to google them.
Something like this comes to mind http://www.newegg.com/Product/Produc...82E16817151085
, but there are a lot of power supplies under $30 that will also do the job. If you live near a microcenter, they have lots of overstock PSUs that they sell for a really good price.