Sorry to hear that, idykenano. Sounds like your eMac's CRT fried just like mine did a long time ago. But I bought myself a nice 20" LCD and hooked it up via the VGA out and it worked fine.
However, you will want to enable your eMac's hidden screen spanning ability, otherwise you will be limited to the CRT's resolution limit on your external display. I used the
Screen Spanning Doctor to enable this, though it looks like it hasn't been updated in a while.
The only issue here is that the eMac will still "think" its internal CRT works and if you're using extended desktop mode (as I suggest), sometimes it's a pain to upgrade the OS or the like because it will insist on trying to display the image in the broken CRT instead of the external display. The solution here is either to disable the extended desktop before hand and re-enable it later, or simply to play "drag the invisible window" till you actually catch it and can drag it on to the new display. I actually got quite good at it after several times. :-P
But don't worry, I didn't find this to be a problem in everyday operations, just when upgrading the OS or otherwise starting from an external disc.