It could just be that today's websites assume a computer several generations beyond what you have, that is the majority of the problem, but how does it seem to perform otherwise? Given the limitations of that hardware, do other programs seem to work more or less as expected?
I ask because with a unit that old, there's a decent chance the HDD is on its way out, but if that were the case you'd be expecting to see a lot of the spinning pinwheel, particularly during tasks that involved using the HDD. So opening an app for the first time, opening a file, saving a file, that sort of thing.
Also, Mac OS X is not free, but you should have gotten copies of the restore discs with the computer. Unfortunately that unit is so old that Apple won't likely even sell you replacement discs, and all replacement discs are locked to a specific unit type, so you would need discs specifically for an iMac G4.
If the HDD is going out on this thing, it's really probably not worth the effort associated with replacing it. Working on these units can be a bit of a trick, even by Apple's standards. Short of a special foam block to keep from snapping the display stem, unless you have a means of holding it upside down indefinitely while working on it, you'll need to take it somewhere, and given the age of the unit, the repair costs will probably be 50-60% of the unit's value if it were working perfectly.
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