This is for a tray-loader CRT iMac, not the newer slot-loader CRT iMac.
You remove the bottom panel from the iMac. You will notice several connector cables that go from the "carrier" (the housing the holds the drives, motherboard, and CPU card) to the rest of the iMac. There will be two or three, depending on whether your iMac has an infrared port (IrDA). One of them is a video cable. If you want to see if your iMac will boot up with the video disconnected, disconnect this video cable and start up the iMac. If it sounds like it is starting up properly, then this procedure should work (you should be able to shut down by pushing the power bottom and the hitting Return).
You simply need to connect an external VGA display to the video connector on the carrier. The problem is that it is an old style Apple video connector, not a standard VGA connector. So you can get one of these adapters on eBay
http://cgi.ebay.com/New-Switchable-Apple-Mac-to-VGA-Video-Adapter-TVCS-183_W0QQi temZ250073333243QQihZ015QQcategoryZ3759QQssPageNameZWDVWQQrdZ1QQcmdZViewItem
I don't know about this particular vendor, but these yellow ones with one switch work very well and they are cheap. Set the switch to the side that says VGA/G3.
Connect the adapter to the carrier and connect the VGA cable to the adapter. This should drive a standard VGA external monitor at up to 1600x1200 (if your display is big enough). The other standard resolutions down to 640x480 should be supported.
That should you get it going again. I went one extra step and removed the non-video components from the system, and set them up on a shelf above my 19-inch external CRT. That is a more complicated process that requires taking apart the iMac. But it works very well.