Oh yeah, Zotac ION board with power brick. Damn, I have one (Atom 330 with ION and power brick, brand new) and was trying to sell it for $135. Oh well.
Most cases are made with power supplies so you can just leave them out. Since you are using desktop drives...
Perhaps consider the cheap Apex cases (MI-008, MI-100) or the Rosewill/Thermaltake rebrands. Those are cheap and look decent, and can fit desktop drives. Just set aside the PSU. The only drawback is lousy ventilation.
In Win and Foxconn also makes some ITX cases that use desktop drives, and which also comes with PSUs that you'd remove.