This is not a Linux problem.

However, my HP EliteDesk G1 800 SFF desktop has 2 display ports, and they are both offset too low to get a cable in either of them.

I opened it up, and the display ports are protected inside a little metal box that is attached to the circuit board. I took a plastic pry tool and tried to bend them both up, from the outside, but no go.

Any one else seen this problem?

Everything else lines up on the back. I don't know how hard it is to take the rear panel off these machines. I am considering taking a Dremel to it.

Addendum: I just tried to put a usb thumb drive in the 2 usb ports below the ethernet cable - they don't line up either.

For reference: https://www.youtube.com/watch?v=cqsWA-2Hquo

No.

In your honour I looked at images of this box, which showed one vga port over one serial port. Nearly everything like that can be solved by spacers, or a few washers. Your box is a desktop. Put books under it.

I took all the screws out of the main board, and was barely able to move the ports so that they would allow cable connections.

Solved

One fix would be to see how much the motherboard needs to be shimmed up, then place a plastic sheet (or washers) of the needed thickness on top the screw posts along the back edge of the mobo.

The better fix would be to remove the mobo and (with most PCs) the insert on the case that has the slots in it to expose the ports. Dremel out the slots enough to allow things to fit, then reassemble everything without adding the shims.
If the case does not have the removable insert then dremel out the slots in the case as the better answer. From what I was able to find it apppears that case may not have the removable insert.

I would never allow the machine to sit for any period of time with the screws removed from the mobo. If it was moved and the screw post contacted a live point on the mobo it could become toast. Just plugging in or removing cables would move the mobo inside the case.

Agreed on not leaving the m/b loose, but a few washers on each mount should space it up.