Remove from dash & Use a multimeter to see if there is voltage on the plug. Check the appropriate fuse(s). On the 7p , your vintage may be different, there are several modules that make up the system. If one isn't working the other in the chain doesn't power up. A fiber optic link can be used to bypass the faulty module to prove which part is defective. VCDS would probably help pinpoint it to.

VW Touareg infotainment fault diagnosis - YouTube

 

There is a fuse on the back of the radio, under the connector.