Sounds like battery is not charged. Remove and clean as others have suggested, use a contact cleaner with lubricant as well. The bike cradle may be corroded, work some contact cleaner with lube into all the pins, excercise them up and down to get it down around the pins. Clean contacts on bottom of Zumo with an eraser and use contact cleaner with lube there too (do this two or three times a year). Put it on the cradle and if it starts up, let it charge for 5 minutes. Remove from cradle and check battery charge condition on the main screen. If low, then it was a contact problem.
If it still won't boot up, charge it on a USB charger for half an hour, remove and try booting up, again check battery charge status. If it is only partially charged yet boots up, it is a contact problem or problem with the cradle.. Of course, fully charge it now that you know.
If it still won't boot up, perform a master reset by pressing the bottom right corner of the touch screen while powering on (press and hold power button for a few seconds then release). You will lose all user data (trip log, etc.) and will have to reset your preferences/audio settings.