Good idea but remember that old computers were not much power efficient. In this and other scenarios you should evaluate how much you'll pay for power and compare it with the cost of a new appliance plus its probably smaller power bill. I confess I didn't research media center solutions but in this case a HDMI compute stick would probably consume far less power than a Core 2 Duo laptop (you might have something more power efficient). You must add the cost and power bill of the storage, unless it's already available and on for all the time you'll use the media center.

I did this, but with Plex (I am a Plex user across multiple devices). I use the computer in clamshell mode with HDMI to my living room TV.

Also, I use Rowmote[0] to control the computer -- an old Macbook -- from my phone and run OpenEmu[1] next to Plex for a home arcade solution. I use a Bluetooth PS3 controller for the arcade. SNES works great with Sixaxis controllers, N64 is possible. Havent tried Dolphin[2] yet... But looking forward to it.

Late 2011 MBP for the curious, runs great for the above uses.

0. http://regularrateandrhythm.com/apps/rowmote-pro/ 1. http://openemu.org/ 2. https://dolphin-emu.org/