Have you tried holding the power switch down for 10 seconds?

Yep. Nothing happens. 

Contact the Support Centre in your country.  There have been a few cases of early units going dead and being replaced.

Assume the battery is charged?

I have a replacement coming for mine, from some posts on Reddit, seems a fair number of Roams are just dying.  Mine went offline, orange charge light never turns off with any USB C charger and won't charge from the official wireless charger.  I can't restart, reset or power it on.