I'd try Goldmemory. It was faster, for me, and found what others did not.
It could be a bug. However, hardware "functioning correctly" can still be an issue. I've had PCMCIA cards that would not work, requiring memory areas the mainboard designers had already allocated. In older machines you'd sometimes need to adjust physical IRQ pins, when adding or removing hardware. Even then, somethings just didn't get along.
With Dos, problems can hide and then show up in protected mode. Dos is just a very un-informed/un-entangled kernel. Since you are using Dos, I might point our SvarDos. It allows Win3x to run (enhanced), provided you know how to modify the WIN.INI file (if needed).
Maybe you've already tried this, but I earlier mentioned the legacy kernel. I'm not sure if the Vesa Local Bus could be causing an issue (I've not had one to try). I've read that the generic kernel does not support those devices any more; but maybe that only matters for X/Way. The modem could be bad, and causing problems; storms used to take those out all the time. One thing you can try, is hunting down the bios utility floppy (I think this machine used one). It may allow you to disable the modem and sound card (for testing only). If disabling isn't an option, then you could try changing the configurations. If the battery ever got low enough, the settings may have gone to a default. Or, at sometime, someone could have played with them, creating a hardware conflict.
I have a laptop, that can run Windows 98 via the USB drive, as long as I load the Windows device driver "Unsupported Device" for the USB hardware. Other machines never give me a chance "Windows Protection Error". Some might call Windows 98 "itself" a bug, but the difference between the machines is just hardware functioning correctly.
I don't know how much more information it would provide you, but the machine does have a serial port. If you are invested enough, you could try debugging from another machine. You'd need a debugging kernel.