Check setup() for something like : while ( !Serial )
If it has code like that it would explain what you see. It won't leave that while() until USB is activated. When USB generally desired - but not required something like this works well - in this case it waits up to 4 seconds and then continues: while ( !Serial && millis()<4000 )
AFAIK: The AGND is meant to be separate clean ground from AGND and shouldn't be tied together
This power issue was solved by holding the part in reset when the power is turned on with a capacitor - see the thread here: https://forum.pjrc.com/threads/42446...-3-6-with-3-3V