Yes, I strongly suspect it will resolve your problem.
The boot.img contains the kernel (and more); because HTC haven't given us full S-OFF, recovery can't write to the boot partition. This means when you flash a ROM in recovery it doesn't replace your stock kernel with the one that should be in your new ROM which, generally, means it won't work. To get around this you have to flash the boot.img that goes with your ROM from your computer using fastboot (similar to the process you used to unlock your One X in the first place when you used fastboot to flash an unlock token).
You'll generally find the boot.img inside the ROM zip, although depending on the ROM the developer may also offer it as a separate download. The fact that you mention trying several different ROMs makes me think you've paid at least a passing visit to XDA, in which case the ROM(s) you tried should have had instructions in the post you downloaded them from regarding flashing the boot.img (as well as multiple posts explaining the process), but if not here's as a quick overview (assuming you've still got the fastboot executable/binary on your PC from when you unlocked, and a copy of the boot.img from the ROM you're installing):
1) copy boot.img into the same folder as the fastboot binary
2) turn your phone on in fastboot mode (turn it off, hold vol-down and power on and it should boot into bootloader; select 'fastboot' from the menu if it doesn't automatically load into fastboot mode)
3) connect the phone to the PC via USB (the text on the phone should now say "fastboot USB")
4) on your PC open a command prompt and navigte to the folder containing your boot.img and the fastboot binary
5) run the following command: fastboot flash boot boot.img
6) run the following command: fastboot erase cache
7) from the menu on the phone select 'hboot', then 'recovery'. The phone will reboot into recovery, then just flash the ROM as normal.
That should be it. You'll need to do this each time you install a new ROM, and also if you're restoring a nandroid backup (copy the boot.img from your backup folder and follow the same procedure).