On an eMac, I'd say no, because then you're going to have to be very careful not to touch the high voltage parts of the unit. Even unplugged, it can store lethal charges for days at a time, at least. You so much as accidentally brush against the wrong part, you might be waking up on the other side of the room, if you wake up at all.
Your problem sounds more like a software issue. Try doing another fresh install, and this time eschew all the "maintenance" stuff. Programs like Onyx and Cocktail are designed for very specific purposes, not general maintenance. They're not quite on the same level of scam as registry cleaners for Windows, but they're not too far removed. People tend to look at them as these miracle cure-alls, and the reality is that if they're not used properly, they can create problems and/or exacerbate existing problems. Mac OS X is based on Unix, FreeBSD to be specific, which can trace its roots all the way back to the original BSD Unix. All Unicies (and Unix-like operating systems such as Linux) have a large number of general maintenance programs that run automatically in the background. There's no reason to run programs like Onyx or Cocktail unless you have a very specific need. That very well could be the source of your problems, or at least a significant contributing factor.
So download a copy of the 10.4.11 combo update (just save yourself some time later), then do a fresh install of just the core apps you need to function for say the weekend. Keep everything to a bare minimum. If you don't ABSOLUTELY NEED this or that program, don't install it. Just update to 10.4.11, and those handful of absolutely necessary apps. Don't copy over the programs from the archive section, install them as if it were a brand new computer. One other thing, is once you've got the OS installed, go into disk utility and unmount the internal HDD (I'm assuming you're installing to the external) just to make absolutely sure you aren't running a program off of the possibly dodgy internal drive. Once you have a bare minimum OS install, you can spend a day or two evaluating things. And again, be sure NOT to use programs like Onyx or Cocktail this time.