Greetings,
Welcome to the forum.
I am not a HP employee.
I would start by updating your graphics drivers. I can't tell you what driver you need because you have not provided the full product number for your PC. I don't know what graphics card you have.
Double check all cable connections. You stated Geek Squad could not replicate the problem.
Then try running HP UEFI Diagnostics to check all hardware.
Power on, tap "ESC". Then select "F2". More information on HP Diagnostics can be found at this Site. (Link).
You could always try a different HDMI cable to eliminate this as a possible cause. Or try the new HDMI cable on a different PC. New stuff can sometimes be defective.
Can you try the new monitor on a different PC to cross this device off the list?
Maybe there is a manufacturing problem with the motherboard. I'm just tossing it out there for consideration since you have had the same problem (if I am understanding you correctly) with two PCs bearing the same product number.
Regards