Most likely the GPU is causing this problem, I’d suggest installing rEFInd (see here) which should fix the keyboard issue that prevents you from summoning the boot menu. Once you get the boot menu, select the fail safe graphic driver to boot Haiku in VESA (framebuffer, actually).
If that doesn’t fix the issue, the only solution would probably be flashing the internal SSD directly or booting via a Haiku DVD.