Have you tried to connect it to your PC to see what happens?
The OUYA has both USB and micro-USB ports, but I've only used the included micro-USB cable to connect it to a PC. There's nothing special about the OUYA connection though, it's the same as any other Android device, and can be accessed and .apks uploaded with the adb tool.
Here's an adb logcat dump of the OUYA booting: http://pastebin.com/NYy2p0NH
And the back side connectors, if you haven't seen it yet:
I'm not sure the micro-usb will have enough throughput to stream from pc to tv. However, if you get the Ouya on the same LAN as your PC, I'm sure it would be technically possible to make an app that lets you stream
I would wager that this is only due to the dev consoles being such early releases... but it was a little frustrating to see all the instructions for Mac connectivity and nothing for Windows/Linux (YET!).
Still, once running, it's an awesome piece of kit :-)
On windows 7 I had to install my device as a generic "Android Testing Device", but it didn't need anything more than a modification of the adb_usb.ini file. There is a whole huge thread on the ouya.tv dev forums on how to get Ouya working on wind 7 if like some ppl you had problems, but it took me 30 minutes of messing with settings to find a solution. Hardly a show stopper