I concur with BD--the eMac uses a video chipset integral with the logic board, not a discreet card. Very typical of Apple's consumer/educational computer lines.
There were some video hardware issues with eMac from Day 1. The very first model had no video or "collapsing" video that was eventually traced to a bad batch of IVAD cables. New IVAD cables are available but are getting hard to find with the recent closure on one of the best eMac service/parts centers recently.
Later, eMacs with USB 2.0 logic boards running 1.0gHz and 1.25gHz processors had a near-fatal logic board issue that could mean no video. Rather than my clumsy fingers retyping everything, please see my post of 15 Oct in this thread:
https://discussions.apple.com/thread/5446791?tstart=0
It shows how to find your serial number, how to tell what eMac variant you have (helpful for us to know), and the ranges of serial numbers affected by the logic board issues with the USB 2.0 models.