These things are so flaky to install OS X on (for very many of us), I can understand why - despite understandable protest - Apple were reluctant to offer OS X support for these old-world machines.
I was doubtful, but one of the few people who bothered to try to help me with this suggested I just install Jaguar on my B&W and then boot the beige from it. But sure enough, I start with the "X" key pressed and it blips an OS 9 screen, chimes, and boots the Jaguar screen! Finally!
The problem now is that the Jaguar boot screen appears on the built-in video out, not my Rage128 card. And then, as soon as the gray boot screen finishes, as the login window is supposed to start, the monitor goes black! The OS does keep loading though.
I have no idea how to configure Jaguar to use the Rage128 video. OpenFirmware defaults to the card, but Jaguar doesn't. I can boot from the OS 9 CD, so if I knew that I could edit a file or move some things around, it might be possible. I took the "RagePro.kext" out of the extensions, hoping that with no driver it'd boot with the Rage128, but no such luck. I wish I could remotely log in to this machine and fix it.
At least it runs better than it did yesterday!
There are known issues with Beige G3's and video support. You might have better chances if you use XPostFacto to install OS X. My Beige refuses to boot from a Mac OS X CD any longer and so I think XPostFacto is the last hope.
Apparently the built-in video of the Beige G3 gets flakey when more than 192MB RAM is installed. There is a technical note about it on Apple Knowledge Base. But the usualy symptomn was that the machine would work fine then the video would cut out. The rest of the system would work for a bit then crash. Having the other video card attached would solve this problem as long as nothing is attached to the onboard video connector so it remains inactive.
However, I don't think I would suggest installing Mac OS X on another machine then swap hard disks. Not unless the specs are the same. (ie; Beige G3, Beige G3.)
Try XPostFacto, it should help out.