first thing you need to do is take a clone of the disk. here is an explanation (if needed) and links to free products that will do what you want
http://www.techsupportalert.com/best-free-drive-imaging-program.htm. Obvious reason being - you have a full backup if it goes TU.
as I'm sure you know, if you are booting on a different machine then the hardware abstraction layer (HAL) will be different and the OS can't cope and BSOD - which is what you are seeing.
once you have your clone and as you have rightly said, you're going to have to put the hard disk in another system and boot from the SBS2003 install disk and let it detect the current installation. you should then have the option of repairing the installation which should resolve the issues that are preventing it from booting.
main thing is - TAKE A BACKUP BEFORE YOU START!!!