Impossible to say considering the OEM computer does not tell us the brand or any more details on the power supply it currently has in it. Most OEMs will cheap out on the power supply so it is likely not reliable or good quality anyway. The main power draw is the 5770. Generally a good 680W PSU should be enough but I don't trust OEM power supplies so I would upgrade anyway. A good corsair, OCZ or antec earthwatts 600W PSU should be more than enough.
On a separate topic, the additional ram will provide no performance gain in today's gaming and certainly not in other activities. It would be a waste of money. If you are gaming you would be better off spending the extra $115 on graphics.
Edit: If you don't like your spelling you can edit it by hitting the edit button at the bottom right of your post.