You need a PSU with at least 30A combined on the 12V rails for that card.
The Smartpower 450W has 15A+17A on two rails, but combined that's only 22A, not 32A, sorry.
This $60 OCZ StealthXstream 600W can handle it without problems. It's pretty good quality, especially for this price, and it's physically small enough to fit even in the kind of HP boxes they sell at Best Buy. I know because I used one that way http://www.newegg.com/Product/Product.aspx?Item=N82E16817341010
Edit: crazy idea - I don't know if the HD 3850 fits physically in your case. Please measure first...