Finally, after some research, I found out that iMac G5s (and early Intel iMacs) are equipped with bad capacitors that tend to overheat and blow up after a while. And indeed, after opening up the iMac's case, I saw that several capacitors did blow up and had some dried gunk on top, and a couple more were going to pop in the near future (the top was bloated instead of being flush).
Unfortunately, the extended warranty that Apple offered because of that issue expired last December. However, there's a silver lining: according to MacBidouille (a great French Mac website), Apple actually will repair faulty iMacs for free, on a case-per-case basis (this was pretty recent news, from June). That was in France, but there's no reason why Apple Canada wouldn't be as lenient, considering that it's actually a widespread issue and that there's no reason that a 4-year-old computer should be absolutely replaced because of a well-known design flaw.
I'll see what happens next. I'll call the Apple hotline tomorrow (I don't have the iMac's serial number with me right now) and hopefully, I'll be able to bring it at the Montreal Apple Store and have it fixed for free. I do have an alternative solution in case that doesn't work out, one that's definitely cheaper than buying another Mac (new or old) or having it fixed for a fee: buying a replacement set of capacitors and having my father do the repair (he's a former electronician, so he has the technical know-how to do that kind of thing). That would set me back approx. $50 (from the site I found, the set cost $35 plus $12 in shipping).
It's still a frustrating setback, especially since I recently had issues with my Internet connection (I was without service for 10 days). Is it a way for the universe to tell me to not rely so much on technology? But I love my computer, I'm such a geek in that way! (Dear universe, leave my 360 and my DS alone!)
My iMac G5 is dying on me. When I came home Monday night (after being gone all weekend), I found my computer completely frozen. I tried to reboot it. The grey page with the Apple logo would load, but then it would freeze at the grey-blue screen where the OS loading usually occurs. I followed all the troubleshooting advice I could find, including zapping the PRAM, booting in Safe Mode (which works but doesn't solve the problem), and fully reinstalling the system. I did repair some broken permissions, but that did not solve the problem either.