There are a lot of atom or mobile i3/i5 powered mini PCs that actually are powered with a 12v brick, in fact most of the industrial ones are. Small form factor, passive cooling, can play media for you and usually comes with 4x 1/2.5gbit Ethernet, so it can double as a router/switch. Usually 10-15w power draw.
Go to AliExpress and simply search for minipc and make sure it has a SATA connector for your hard drive.