OK, I found a solution which helped me at least, and may help others.
I made another post above which tells of my situation. To make a long story short, I had two XP PCs with this BSOD "7E" error, one was fixed by
removing the KB977165 patch (using the Recovery Console and the "BATCH spuninst.txt"), the other was not, no matter which solution I used in this thread (including replacing the ATAPI.SYS file in the drivers folder).
What I did was hook up the hard drive to another XP PC as a slave, renamed the \windows\System32\Drivers folder on that hard drive to something else. Then copied the entire "Drivers" folder from the working PC to the malfunctioning hard drive.
When I put the hard drive back into the original computer, it booted right up, with a number of driver errors of course. I reinstalled all the needed drivers (network card, video, etc) and everything was back to normal.
I did a complete scan on the hard drive and did find one virus. I have no idea if this, in combination with the MS patch was the cause of the problem or not. It was a "Trojan horse Generic16 GDA" virus, and the virus file was in the user's "Application Data"
folder called "syssvc.exe".
So, the problem most definitely lies in something in the "Drivers" folder. I didn't want to spend a week sorting through which file that was. Hope someone else can find it.