Solid red LED indicates No local or Internet connection.
If you hold the button down for 40-45 seconds it should blink yellow, this is a power cycle. Do this while connected to power (connected to the base plate). Does the LED change at all?
Removing the camera from the baseplate will eventually drain the internal battery.
On the back of the camera you should see a label, is it sitting flush or is it being pushed out? Feel free to post a picture