For that budget you're more likely looking at a desktop case rather than a specific HTPC case which tend to be a lot more. Maybe there's some marketing involved in this?
The Antec NSK2480 comes to mind. It is also used as the basis for the 'Fusion' HTPC case but is more basic and is really just a Desktop case with a sleek front. The included PSU is quiet but not silent and cooling will probably require some 3rd party 120mm fans to make it quiet but the price is good.
Pushing the budget perhaps but for silence it'll be unbeatable, what about a Streacom FC5 or FC10? Then you can do things totally fanless with those components.