Very strange to hear. I type this text from my Powerbook G4 1.67 GHz / 2 Gb RAM ( sometimes after start there is only 1 Gb RAM - lower memory slot problem....), latest tenfourfox - and i can say, internet browsing is painfully slow there -even on relatively simple pages without lot of ads and flash....
safari is bit better than tenfour, but there is no updates for it, as so, many sites do not work with it, as you mention, and in anyway - it is too a bit slow. yet, in general, that is very good machine, 10.5.8 OS X, 40 gb hdd, 15" screen, and very nice "pages" icon...;)
but very slow for internet, youtube plays with heavy freezeings, even small resolution videos, and so on, sadly...;(
buy this a 2 years ago for try to discover who is Mac OS ( my old dream, i start my computer world with zx spectrum 48k, and then there is Amiga, about what we can only dream...;) ), and it like me or not. In result, now my main machine is mbp mid 2012 13" - so good, as i turn on my linux slackware desktop computer about a one time in month or so..;)