Is this the 1.25 GHz retail model (Radeon 9200) or the 1.25 GHz education market model (Radeon 9600)?

Are you able to see the GRUB menu?  When does the screen turn black?

After the screen turns black, does there appear to be further disk activity?

Are you using Mini-VGA or the built in display?  Has this machine ever used something like Screen Spanning Doctor, which enables extended desktops instead of mirroring in Mac OS X?  If so, have you tried resetting the NVRAM (which will temporarily disable the extended desktop patch until applied again)?

You said “just about any modern Linux distribution”; do older ones work?  Can you provide a list of what does and doesn’t work, so that we may narrow down kernel versions?

I’m trying to find someone locally with an eMac 1.25 that can loan it to me for more hands on testing, but I’m not sure I will be successful.