According to version tracker ( http://www.versiontracker.com/dyn/moreinfo/macosx/10596... ), firefox 4 beta 1 is supposed to support PPC Mac 10.4, but for me it crashes on startup. Does anyone else have this problem with a PPC mac running OS X 10.4? Has this bug been reported? Is there plans for PPC support for Mac OS x 10.4?
I am running Mozilla Firefox 3.6.6 in a Macintosh with 10.4.11, I know this is not the version you're talking about but it is a fully tested, stable product. Is there any specific reason you're using a beta version of Firefox? If it crashes, you should let Mozilla know about it so that hopefully they can work on the problem and fix it before they have the final release. I'm guessing it's too early to tell whether they will support 10.4.11 but waiting is the only option for now.
UPDATE: Downloaded that same version you suggested and tried in my iBook G4 1.33Ghz and it just crashes on launch just like what happened to you. I wouldn't be surprised if they didn't support OSX 10.4.11 after they said they would. I remember when there was talk about 3.0 being supported by certain Macs, mine being one of them at the time (I think it was eMac 700 with OS 10.3 yep) and later we found out that no go; I upgraded OS to 10.4 and it worked though.