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.