How to connect dual monitors to iMac?

Is anybody knowledgeable about iMac G4s and how to fix the black monitor/salvage files from the system?

• So I use an iMac G4 model as my drawing computer, since I'm an aspiring digital artist. It's not hooked up to the internet, so there's no threat of virus contamination or anything, all I use it for is drawing from bought-and-paid-for programs, no sketchy illegal downloads or anything. I've had this iMac for about seven years, and in the entire history of its life it has only blacked out twice, once about two years ago, and now again about four months ago. The first time I thought that I'd killed the hard drive (because after it blacked out I tried to call Apple, and during a mix-up over trying to get the serial number I whacked the main computer pretty hard, and thought therefore that I'd erased everything. We've never put the old hard drive back in to see if it does indeed work) and so we got a new one. There was a load of dust inside the little brain-hull computer base thing, and so we blew all of that out of there, put the new hard drive in, and it worked good as new. Now it's doing it again, and I am extremely sure that it's not the hard drive at all this time, because I haven't messed with the computer aside from restarting it like Apple Support said to to see if it was just a momentary glitch. I have no idea how to fix this problem; I've been rooting through Apple Support's articles on the issue and I'm so completely computer-illiterate that I have no idea how to proceed on my own, and I can't afford to hold hours-long conversations with Apple staff members, half of which will take place on hold (like I had to the first time (which also accomplished nothing.)) My main concern right now, though, before trying anything drastic with the computer, is getting the files off of the computer. Like I said I'm a budding artist and I have many, many valuable files of sketches and unfinished projects locked away in the hard drive of this computer, and I'd really like to get those off with as little risk to them as possible. While researching THAT part of the issue, I was told by some help article that you can attach the computer to the external monitors of different Macs to get whatever you needed secured dealt with before going in and checking out the guts. At first that sounded great and I tried to connect the drawing computer to the internet computer, but the pesky G4 has some incompatible plug-socket thing that won't attach to the cable that we have! So then there was some rumor that there's ANOTHER cable that's compatible on one end with the elitist G4's stinking back panel AND with any other computer you care to jam it into. My dad thought he'd hunted one of these down, but, after forgetting to for several days, couldn't trace THAT cable again, so now we're back at square one. Basically I have no idea where to go from here. I'm a completely computer-ignorant fool, when something goes wrong I throw a tiny tantrum and dissolve into tears. Those files are of extreme importance to me, and I would appreciate any advice anybody has to offer on the matter. ... Happy New Year, at any rate :)

• Answer:

  Don't get sidetracked with the advice about a Linux live CD. It will be a waste of time and money. Connect by Firewire cable to another Mac that has Firewire 400 (older style Firewire) using a cable like the one at the link below (You can buy one at any modern computer shop, such as Best Buy or Fry's). Restart the iMac while holding the T key for 30 seconds. The iMac HDD will mount on the other Mac. Then it's just a matter of drag and drop. A common cause of no video on a computer that is five years old is a weak / dead battery. See the 2nd link below. The battery is half AA size, either green and white or purple and white. When you go shopping for the Firewire cable and battery, buy an external drive also. I sleep well each night because I have a backup copy of EVERYTHING important.