Okay everyone here is the latest plan of action, after discussion with DW, an DN.
After abundant amounts of time in researching this problem here at AMHD, and at other sites.
I have found more information on, and a way to reset eMachines. See: How to Reset an eMachine Computer | eHow.com (http://www.ehow.com/how_4829262_reset-emachine-computer.html)
After SG's #9 post, Cb's #11, and SG's #12, I thought back to the sequences of rebooting the PC.
The PC never did fail to reboot, and as it was doing so, each time I saw the moment that the option to press F11 would occur, (i.e. "Press F11 to start recovery 1 ”)
In deference to d_h's #13 post I will also try F12, if the above attempts fail to produce results, although with following the PC's on-screen instructions I strongly feel that, that, procedure will produce the desired effect of entering the reset process.
Once that is achieved I will follow the steps outlined in the above link, onward to a successful outcome.
There are several other caveats to be aware of with eMachines:
A bad power supply, notorious for this, especially Bestec
If it has a AGP video card rather than the integrated on-board variety
A bad motherboard
If everything runs normally after reset/recovery, okay, good.
But right before every time it locked, the display would split into an RGB “ghost effect” similar to looking at 3-D without the glasses that would lead me to believe that the video card was receiving an unregulated supply of power or it could have the AGP type card., that will then need to be tested.
Borrowed from post #2 here: Power supply or motherboard symptoms - Geek.com (http://www.geek.com/forums/topic/power-supply-or-motherboard-symptoms)
"then Look at the large chips and heat sinks (apart from the CPU) to see if either has pulled out. There are four U-Bolt-shaped connectors on some models... at the video chip set heatsink. Sometimes one of these will pull out ruining the board."
For now it's just a matter of scheduling the time to get back to our DN's home to do the deed.
I would like to thank:
seahwk83
Curlyben
ScottGem
desire_harya
For your invaluable insight, time, and effort to help me, and for giving my brain a jogging exercise.
Not sure when this will happen, but I will post further updates.
k