Try these steps:
Wipe down the back of the Starling with a damp cloth, let it dry, and try charging again. If dirt gets stuck on the back it can block the charge from coming through.
Try syncing while your Starling is in the dock to see if it’s Battery is increasing. If not, try using an Android cord?
When charging, do you see the light indicator on the dock? If yes then your Starling is charging and it may be experiencing another issue.