You won't be able to handle games like Crysis or Supreme Commander with that system, you should be fine with older games though.
I would however, highly recommend a better PSU, as generic power supplies are often unreliable and can lead to damaged hardware.
You should view the information located here:
Power Supply Information and Selection
And use it to choose a new PSU.
Your system will not need a very large PSU, so I would choose one from the "Power Desktop Computer Class".
Hope this helps.
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"Come forth for the cattle call
Confront the evil river you can't control
Wicked ways and venomous eyes
Just human nature in disguise..."- Clouds over California