Welcome!
With 1Gen eMacs the biggest known bug was a bad IVAD cable in the video hardware. If the computer makes "all the right noises" but there is no video, the cable is suspect. Symptoms were no video, staticky video, or an image that seems to collapse from side to side. Depending on where in the world you are you can still find replacement cables but the change-out forces you into a serious takeapart and working in areas where massive voltages are retained in the video hardware. I cannot recommend that anyone attempt this without deep familiarity with and training in safely servicing high voltage CRT video systems.
Here are some old Apple links regarding eMac issues:
This one applies to 1Gen emacs: eMac: Popping Sound Followed by No Video - Apple Support
This one is for 2Gen: eMac (ATI Graphics) - Distorted or Shrunken Video - Apple Support
Also the IVAD issues seems to affect mostly 1Gen eMacs made before Aug 2002 so pinning down the week of prodcution could be very helpful in eliminating some problems. Note! the following requires you to look up information based on your serial numbers. Post only the results, not the numbers, when you respond!
Pry open the optical drive door with a fingernail to find the serial number on a paper sticker:
Go to this web page: https://everymac.com/ultimate-mac-lookup/ and enter the serial numbers. The return should include the week of production. Let us know when that was but, again, please do not post a serial number in an open forum.
We have two working eMacs here. The 1Gen was made in August 2002 and never showed the IVAD cable symptoms.
