To start, can you connect the monitor to another PC to verify it works correctly? If so, then we will move on to the HP PC.
Your HP micro tower is a business class computer that can come with many different hardware configurations, so I have no way of knowing what you have exactly.
So to clarify which ports you should use... If your PC has a dedicated graphics card installed, it will have a video port located towards the bottom back of the tower. Number 10 on the image. You have to use that one.
If it does not have a video port at number 10, then you have to use ports 3 and 5.
Reboot the machine and rapidly tap F10 to enter the bios. If the bios screen appears, that's a good sign. While there, reset the bios, save and exit.
See if the PC will light up the screen now.
IF the bios screen is also blank and nothing will show on the screen, then the video card is most likely failing.
If you are under warranty, you can contact HP Support for warranty service.