Screen problems like that are often hardware problems. Can you correlate the failure with temperature--like the time from cold start to the problem appearing? If consistent, there could be a thermal effect happening. Heat causes some component to fail.
Please run System Profiler (in Applications > Utilities) and see what its first screen reports for "Model Identifier." It is the second line in the image below
The reason for doing tis is that there are two version of the 1.0GHz eMac. Most will have the Model Identifier "PowerMac4,4" but there were a few 1.0G models shipped for edu-only use that had the identifier "PowerMac6.4" (indicates a USB 2.0 logic board) The latter were not shipped to commercial accounts but have appeared in private hands as schools shuck them off when they upgrade hardware.
The 6,4 variant with 1.0 and 1.25Ghz processors had a near-fatal logic board problem usually (but not always) found in these serial number ranges:
- G8412xxxxxx- G8520xxxxxx
- YM412xxxxxx - YM520xxxxxx
- VM440xxxxxx - VM516xxxxxx
If you have the 6,4 identifier, see if your computer falls in these ranges.
The very first eMac 700s had a bad IVAD cable that caused video problems but that was fixed long before the 1.0ghz units were developed.
Also, I have the rear of the machine (where the air vents are) pressed up against the wall. Perhaps I'll start by moving it away from the wall a little to see if that helps.
By all means try to get it about 6 inches (~15cm) from the wall. Even though the shape of the case means you can't completely occlude the exhaust flow this way, it could reduce the effectiveness of the exhaust function especially when combined with the Fanmate.
We have a geriatric PowerMac 6100 that exhausts out the bottom, It struggles even on a perfectly smooth surface. I have to set the case up on 5/8" spacer blocks for it to even run. So exhaust efficiency can be an issue.
As for its working for a while and then failing, it could be that long-term exposure to the extra heat caused by the reduced fans speed and the proximity to teh wall has damaged some component. Cable insulation can get soft and flow, exposing wires, and logic board component can become cantankerous. Right now, I'm betting on a cooked video cable, but haven't been inside eMacs enough to say which one.
I understand fully about the noise issue. At one point, I had a G4 MDD tower and my wife had her 1.42Ghz eMac on the same workstation. I felt like I worked in a shop where aircraft engines were tested all day! Now we both have late-model iMacs and the noisiest things in our work area are two external backup drives and empty stomachs demanding attention!
Lets see what improved cooling accomplishes and go from there.