As you have learned, when you installed SuSE to an external drive, SuSE detected the hardware for that machine. When you move the drive to another machine, it has different hardware, and the config files are wrong. But, you do have command line to work with.
1) you can run sax2 to configure graphics for the machine you have moved the drive to.
a) Study the man pages for sax2 to learn what options to pass
b) Use the search function on these boards to search for sax2 issues for discussion on the topic.
c) use
www.google.com/linux for Linux related issues such as the use of sax2.
2) SuSE has modified grub a bit, such that, at the boot screen, you have a boot prompt under the list of operating systems. You can pass parameters to the kernel via that boot prompt.
Here are two charts of vga values you can try to see if it gives you some kind of graphics on boot.
Colors ( depth) 640x480 800x600 1024x768 1280x1024 1600x1200
---------------+-------+-------+--------+---------+---------
256 ( 8 bit)| 769 771 773 775 796
32,768 (15 bit)| 784 787 790 793 797
65,536 (16 bit)| 785 788 791 794 798
16.8M (24 bit)| 786 789 792 795 799
640x480 800x600 1024x768 1280x1024
----+-------------------------------------
256 | 0x301 0x303 0x305 0x307
32k | 0x310 0x313 0x316 0x319
64k | 0x311 0x314 0x317 0x31A
16M | 0x312 0x315 0x318 0x31B
These should work for all modern monitors. To pass a parameter for the resolution you want, at the boot prompt, type 'vga=792' or 'vga=0x318' for 1280x768 resolution. You can see from the charts that they are the same, just different code (something like hex and octal values) for the same resolution.
If passing one of these parameters to the kernel on boot doesn't work, you may be stuck with option 1, every time you move the drive to a different machine.
Of course, if you are handy at writing scripts, take notes on every step you take when running sax2 manually, then write a script to do it all. Then just run the script when you mvoe the drive to another machine.