If he's determined to stay in the dark ages, it sounds to me like a simple
elimination of Win98 would improve things. A simple addition to the
autoexec.bat file would start the program immediately and eliminate the overhead
of Win98.

My bigger concern would be the age of the hardware. And, I'd guess, he's
running on a single disk with no backups. Something as simple as a new whitebox
PC with DOS 6.whatever on it would likely be an improvement over what he's got
now. It's been a while, but I suspect the autoexec file could also
automagically write a backup of the database to a floppy on shutdown of the
application. Of course, that would make the owner the weakest link coz he'd
have to take the backup off site every day.

If you can convince him to move into the modern age, the biggest single reason
to connect to the web would be for an automated backup to a web-based backup
service. That would require, of course, a hardware firewall between his PC and
the web - but that'd be a small price to pay for not losing his business due to
a PC problem.