Sounds more like a loose contact with the PCIe slot.
From the little troubleshooting that you have already done, it seems that the slot you're using on the Mobo is having a problem with connecting to the GPU.
My suggestion, if you have another PCIe Slot free on the Mobo, use that one. and try it again.
Also check if any of the RAM modules have come loose, that could be another problem with regard to the Beep errors.....