The iPad can be finicky about the connection order - as the HDMI HDCP handshake seemingly only occurs upon connection of the HDMI Adapter to the iPad.
The resolution to the problem is to ensure that all TV/Monitor connections - and connection of the Power Adapter - should be made to the HDMI Adapter before connecting the Adapter to the iPad.
This connection sequence allows the HDCP handshake to enumerate and verify the attached TV/Monitor upon connection of the Adapter to the iPad. If the Adapter is instead connected prior to making connection to the TV/Monitor, the HDCP will fail to detect a compliant monitor - the result of which is no video output.
I hope this information and guidance proves to be helpful in resolving your difficulties.