OK I have diagnosed the problem. It is media related.
The exact "error" messages I got were: under WinXP - "Insert disk" (it didn't think a disk was in the drive). Under Win98 - "Drive not ready" (again it didn't think a disk was in the drive).
So I first tried Daemon Tools as suggested. But as I feared, DT was unable to mount the drive because the OS couldn't read the risk to load it into the virtual drive.
Next I guessed that perhaps the problem was that my burner was on my Win98 box and that my use of 1 GB file splitting of the ISO file was causing a problem. So I decided to test burn a disk with that option turned off. Since this was a test and I didn't want to waste a disk, I used a DVD+RW (Memorex) disk. It worked! The disk could be read by both standalone and PC DVD drives.
So I tried the same settings and burned a DVD+R disk. It didn't work. Same situation (works in standalone, doesn't work in PCs) as before. That disk was burned at 4x. It occurred to me that the +RW disk would have been burned at 2-2.4x, so I tried another +R (4x rated) disk at 2x burning speed. It worked (in both standalone and PCs).
Conclusion - Digitial Media 4x DVD+RW disks are only partially compatible with the NEC2500A at 4x speed. They work fine at 2x.