Lord Sirian

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.