Early eMacs had a known issue that caused the screen to distort or collapse. It was caused by a bad IVAD cable. I am thinking that's what you've encountered. Units most often affected were from time of introduction (April 2002) though fall 2002. Most of the affected units received new cables and later first models never showed symptoms. Interesting discussion here:
https://www.applefritter.com/node/11028
We may be of more help is you can hlep us identify your exact sub-model as, of the four families of eMacs, two had known serious hardware issues. First see this Apple support article:
eMac: How to locate the serial number and identify your model - Apple Support
The lookup table has lost its borders (at least in Safari 11) so this copied image may be easier to read:
Once we know the sub-model we can beter advise a troubleshoting scheme.
If we need to recommend parts, that is easier if you let us know roughly in what part of the world you reside. It does you little good if we recommend a vendor who does not ship to your region.