i wasn't trying to mislead you but there's a certain vocabulary here that we PS2 modders use related to PS2 homebrew and stuff . its clear that you don't have fmcb installed if you tried to install with swap magic by attempting to boot the fmcb.elf. i gave you a link a fmcb tutorial were you can build an iso of fmcb to boot with swap magic.
did you use a sliding tool or is your slim sensor modded? either one of these pre-conditions are required in order to be able to swap using swap magic. if you are able to swap using these methods then perhaps the PS2 disc that you are using does not have the enough "TOC" (table of contents) amount to boot the bios cd that you have. a PS2 disc with a good amount of TOC will boot the burned cd.
perhaps the bios disc image (iso) that you created wasn't build right. i really don't have the time to go over the tutorial that you used but there is something that you missed.
feel free to use the links that i posted earlier to help you install fmcb via a bootable cd with swap magic.
PS1/SCPH-7501 | MM3 modchip
PS2 v9 | 250GB hdd | PS3 component cable | katana 32mb mc
PS3/CECH-2001B | 250GB hdd | 3.65 ofw