You can get in the bios even if you don't have a hard drive installed.
When you first power it up, watch for a message at the bottom of the screen that will tell you which key to press, sometimes F1 or Delete, but have seen F8 as well.
Bios boot order messup is no big deal, it will still POST it just will tell you NO BOOTABLE Hard Drive found.
CTRl - ALT - DEL, let it reboot, go back into BIOS, fix boot order, then Save, Restart and it should boot your OS.
If you don't have output to the monitor you have something else going on like a loose or unplugged monitor cord, monitor power cord or loose video card.
BIOS boot order is just choosing which HD, USB, CD Disk to boot for primary and secondary, has no correlation to the No Output which is the monitor telling you, that you have no incoming video signal...
And changing the MB, will most likely mean a new Windows install...