If the motherboards beep when you have a monitor, and they don't beep without a monitor, don't bother reading further 
Hmm motherboards sometimes want you to press a key if there's an "error", and lacking a keyboard or monitor usually counts as an error. Also, are you sure it's a the monitor and not the keyboard?
Hmm my ASUS Maximus V GENE has an option in BIOS called "Wait for 'F1' if error". If you have something similar you can try turning it off and see what happens.
Hmm motherboards sometimes want you to press a key if there's an "error", and lacking a keyboard or monitor usually counts as an error. Also, are you sure it's a the monitor and not the keyboard?
Hmm my ASUS Maximus V GENE has an option in BIOS called "Wait for 'F1' if error". If you have something similar you can try turning it off and see what happens.