Did you figure out if you have the 4,4 or the 6,4 eMac? The early 4,4 had poorly-shielded internal speakers that could be noisy. However, that behavior would have been there since Day One, not only after you change RAM.
When you pull the RAM, see if any dust is caught in the slots.
Some history of "issues" with eMacs--see if any patterns match:
1) The very first eMacs (Jan 2002; 4,4)) had a defective IVAD cable on the monitor that could cause video artifacts and failure. Thsi was pretty much cleared up by Aug 2002.
2) The aforementioned speaker shielding issues casued video artifacts in sync with the sound unless you kept the volume low or used external speakers.
3) 6,4 eMacs ("USB 2.0") with 1.0 and 1.25ghz processors had a near-fatal logic board issue. Your computer is working too well to have this problem. Yes, it was that bad.
The 6,4 eMacs with the 1,42Ghz processor were the best of the lot and, based on a lack if issues showing up here, were the lease troublesome.
All 6,4 eMacs can accept a total of 2GB RAM with modern modules. However, not just any PC2700 1Ghz module will work. You have to get it from the right vendor. Our 1.42g has 2GB RAM and both modules came from here:
1GB PC2700 DDR 333MHz CAS 2.5 184 Pin DIMM
They have worked perfectly.