My HP 500B MT on dial-up has a network driver that doesn't suppport Windows 10. Is there a motherboard out there that I can use in this PC that will support Windows 10 and dial-up?

You dont need any new MOBO, only a working USB port
a fact
do not buy software modems! (they are no good)
or 1/2 software/hardward (the software side bad like above)
Do use 100% hardware modem USB the above USR 5637
and a free cheap dialer app (ask)
that uses the AT command set see here.

http://support.usr.com/support/sportster/sportster-files/techref_uk.pdf

nothing works better.but, but...
why not get DSL on that same phone line?
never use dialup in 2018 ever.

the dialer talks to the modem on USB port
and off hook commands it.
then dials
and connects automatically and locks up.
its that simple and W10 has nothing at all to do with this.
nor any motherboard, since 1998SE , USB was born.

If your only problem is dial-up networking, then an external modem may be the best fix. Back in the days when I had dial-up, US Robotics was a good brand. Here's one you can look at:
U.S. Robotics USR5637
NeweggBusiness Robotics USR5637 High performance 92 modem 56Kbps USB Data...