What is this?
 

The display is broken, nothing shows on it. I can't get it to turn on.


http://cdn.getauto.com/photos/3/1549...E050437-8c.jpg

Looks like a thermometer display. I don't know if that's aftermarket or RPO. Just so you know, your Coupe was built by Mitsubishi. It's basically the same car as the Eclipse coupe and the Dodge Stealth coupe.
There is probably a Stealth forum and an Eclipse forum somewhere. Those guys might recognize that.

http://www.familycar.com/RoadTests/C...ages/Stack.jpg


Seems to be a factory option. I found several others in Google Images.

Anyone know where the fuse might be for it?

check your owners manual