Re: Windows 7
The geek in me is screaming "No!!!!"
But to answer your question: Windows 7 should work in your setup "as is" and give you adequate performance.
If you're upgrading your OS you may as well upgrade your motherboard as well as the one you have only supports a maximum 1GB of RAM.
You can get a new MSI H61M-P23 B3 Intel H61 Motherboard / Intel Core i3 3.10 GHz Dual Core PCU combo for around $180.00 (+ shipping of course) that supports DDR3 1333MHz memory. Ram sticks are cheap these days. I think you can pick up a 2GB stick for around $24.00.
It's really not all that hard to switch out a MB but if you're leery of doing it yourself most Indi PC techs will do it for you for around $40.00 to $60.00. (If they want more than that price tell them to go pound sand)
And, hey, while your at it a 500w PS isn't all that much more than a 350w and you can then do even more upgrades in the future.
Day by day
Oh Dear Lord Three things I pray
To see thee more clearly
Love thee more dearly
Follow thee more nearly
Day by day