are you positive the beeping is coming from the buzzer on the motherboard?
disconnect the speaker and try again. verify the trail so to speak.
the beeps and the GPU behavior are at odds.
download speccy its a program that will list the specs of your system and post your motherboard and GPU models as well as the power supply information. you may need to open the case to read the PSU label.
Canned Grounding Rant-
shut down system and remove side panel. with the power cable plugged into the PSU touch a bare unpainted metal area of the case. (my favorite spot is an unpainted screw securing the PSU) once you have grounded yourself you can unplug the computers power cable from the PSU and can touch the system.
if you move your feet, or shuffle in your chair, plug in the cord, reground yourself and unplug again.
end canned rant-
I will look over the manuals and see if there is something were missing but I need to know the models.
https://www.ccleaner.com/speccy