2009 mac mini: gray blank screen; boot commands not working

Ubuntu 22.04 should boot that iMac assuming the USB stick is good. Macs can be very picky about the drives used for booting and the quality of USB sticks is extremely poor. At the very least you should be able to Option Boot the Mini to access the Apple boot picker menu even if the internal drive has failed (or the Linux USB stick is bad. In fact I believe you should still see something on the screen even if no bootable volumes are listed, although some hard drive failures may cause the system to freeze that perhaps nothing will show on the screen for the Apple boot picker menu, but this would be rare.

If all you see is a solid gray screen when trying to Option Boot the Mini to access the Apple boot picker menu options, then you have some sort of hardware issue with the Mini. Try disconnecting all unnecessary external devices in case one of them is causing a problem.

Are you installing a Linux distro that actually supports a 2009 MacMini? Several current distros do not support Macs that old and need to install one of the legacy distros.

Are you sure the methods you are using to create the USB are in fact designed to be bootable on a Mac?

Why not try to create a DVD from an iso and use that?

If you cannot boot to the internal drive either, then I would remove the bottom cover and disconnect the hard drive cables from the Logic Board, cover the connectors with some tape so they don't accidentally make a connection. These connections are easily accessible with the bottom cover removed. Try booting from a bootable USB stick (macOS, macOS installer, or Linux). You can also try removing the memory to see whether you get the three beeps when powering on the Mac without any memory. If you get the three beeps, then install a single stick of RAM and try again to boot. Then remove that memory stick and try the other one so you can eliminate memory as a possible problem. Try both memory slots as well. It is rare for more than one memory slot to fail at one time. If none of this helps, then it is probably time to retire this Mini as there are no other easy fixes or troubleshooting tips.

Actually the only other tip regarding using Linux to test boot this Mini is to try using Knoppix and/or the Debian Netinstall (it is usually the default option when downloading the Debian installer). UEFI computers tend to be very picky about how the bootloader is named. I know that some Macs seem to be more forgiving than others. I know that the Debian Netinstall image uses a generic "boot" name for their bootloader. I'm unsure what Ubuntu or other Linux distributions may use/name it. I also know that Knoppix tends to boot just about any older system out there...it is rare that I cannot get Knoppix to boot a computer even an older Mac. This is only about seeing if the Mini will boot since you really don't want to install Knoppix and the Debian Netinstall will require a wire Ethernet connection since the Apple WiFi chip may require non-free drivers not available with the default Netinstall image.