Hang on boot--DOS-based computer to computer data copy?

I have a Windows 98 machine which hangs after the Y/N prompt at
"msmouse.vdx" (I had chosen "4. Step-by-step confirmation" after
having pressed F8, and I chose Y to ever prompt, up to this point.)

I'd like simply to reinstall Win98. But first, I'd like to backup
100MB or so of data from the HDD. One of the files is a 50MB .pst
file.

I can boot into Safe Mode just fine, and the data is there. The system
has no CDR/W drive, no USB ports, but it does have a working internal
NIC. (I don't have access to an Iomega zip drive, so that's not an
option.) I do have access to a dozen other functioning Win98
computers, though.

I'm wondering if there's a way to use a crossover cable to copy the
data directly from a Safe Mode session, or even a DOS session, from
the Hanging system to one of the other Win98 systems. Is that
possible, and if so, what is the command to issue from the working
Win98 computer that would force the copy of data from the hanging
computer? TIA for any ideas.

(I haven't given up on getting the system to boot, but I thought just
fdisk-ing would be easier. But I don't want to lose the data.)