As said the power from the relay is supplied via the switch, it will only do so when the engine is running, on older Ford it gets this feed from the alt and from the ECU on newer cars. The relay is a "Special" relay in that it has a timer built on so the screen powers off after around 10 minutes, unless the ECU can do this, if so it may not have a timer.

So if you don't have power to the switch you need to be looking at the live feed to it for the problem opposed to the relay itself.

Martin