The 12" iBook 800MHz was released in 2003, and so is Rather Old (tm) these days. Sufficiently old that when Apple released OS X 10.5 ("Leopard"), the previous release of OS X (and the last one to support the PowerPC based machines), the 800MHz machines were not supported (minimum 867MHz). This caused some concern for people with the 800Mhz models rather than the 867MHz models in the same range, including myself. The minimum CPU speed is enforced by the installer, after the first language-choice screen, so it is a limitation rather than just a recommendation.
People found a number of work arounds, including removing the disk and installing then returning the disk, editing the installer, but the one that is easiest for the technically inclined is to change the reported CPU speed:
Start up Mac with Opt-Cmd O-F (to enter Open Firmware configuration console)
Enter these commands to set reported CPU speed and boot from install:
dev /cpus/PowerPC,G4@0 d# 867000000 encode-int " clock-frequency" property boot cd:,\:tbxiInstall as normal
(I'd suggest not doing this unless your 800Mhz machine is otherwise fairly capable, eg maximum RAM, etc.)
Recently I lent my iBook to someone (whose main machine had been stolen, while they waited on an insurance replacement). When I got it back I decided the easiest way to get it back to the way it was before would be to restore it from the Time Machine backups. (I also had another backup of the few files on that machine I cared about, so I was willing to risk needing to install from scratch in the interests of science.)
It's possible to do a full-disk restore from Time Machine from within the OS X installer (rather than just individual files from within the normal running operating system). The approach, as described here is:
Boot off the OS X 10.5 (Leopard) install media (eg, as above)
Choose language
Make sure your Time Machine backup drive is connected (eg, external disk, or on the network)
From top menu choose Utilities -> Restore From System Backup
Select the backup disk
Select the backup date (eg, the most recent one, at the top of the list)
Select the disk to restore to (eg, the internal disk)
Confirm the restore, including erasing the destination volume
Wait
On my first attempt I chose to use Disk Utility to erase the existing disk contents, as mentioned in the article, which involves going back to the welcome screen to get it to recognise the new partition as a possible destination, but I found that the restore didn't work and I had to reboot and try again. (To be precise it claimed to work, rather quickly, but the machine didn't boot off the harddrive and I had to boot off the DVD again and have another go. The most obvious difference between the two attempts was on the first one it didn't show the proper logo for the destination disk, presumably as a result of not recognising it completely.) The second attempt took a much more believable time to restore (initially estimated around 3.5 hours for 30GB), and worked correctly. And as I found, the restore process erases the destination volume anyway so I didn't need to worry about doing that myself. (Presumably that step is required only for a brand new disk.)
The first boot after the restore took a very long time (and the internal disk seemed to be fairly busy), so I suspect that there's a few recovery steps required after the initial volume restore when booted off CD. The only progress information is the spinning boot activity indicator (which unfortunately gives no idea when it might complete). Eventually when I next checked on it the screen was blank, pressing a key made it act as if it were unsuspending but the screen display never came back. I forcably powered it off and then powered it on again, and it booted fully. The first Time Machine backup run also took ages (as far as I can tell it had to checksum every file on the disk in order to see if it should be copied to the backup drive). Overall the whole process took over 5 hours, for a 30GB backup, so it's not exactly as speedy as recovering from a full disk image. But useful to know that it is possible in a pinch.
Updated, 2011-04-20: Sadly this iBook died in March 2011. The screen doesn't light up (the backlight had been failing anyway) and/or it doesn't boot (nothing more than the power on chime). As I don't have anything which will definitely mount a firewire disk any longer, I can't even be certain whether the boot-as-disk option is working or not. At some point I might see if I can recover the last few files that were only on that iBook from the Time Machine backup of it.