Find out what program is prompting the dial-up.

First, does this occur even if you don't use the machine after restarting?
In other words, are you *certain* that no program you launch after startup
is responsible?

Next, see my article "Clean Boot: What it is and why you need it."
http://www.grystmill.com/articles/cleanboot.htm

That will introduce you to MSCONFIG, the primary trouble-shooting tool in
Windows 98. Follow the steps I give to set up a Clean Boot environment.
After restarting, just let the system sit there with no input from you
(except to answer prompts if you get any). Does a dial-up prompt appear? If
so, then see my other article, http://www.grystmill.com/security.htm

If no prompt appears after ten or fifteen minutes, then run MSCONFIG again,
and if there are any items besides the Startup Programs that you previously
disabled, re-enable (things like Autoexec.bat, Config.sys, etc., if they
exist and had been previously disabled.) Restart the system and test again.
If no dial-up prompt, again use MSCONFIG to enable just one half of the
items on the Startup tab. Restart and test. If the problem returns, then you
know that the culprit is in the batch that you re-enabled. Vice-versa, if
the behavior doesn't return, you know the culprit is in the half that was
left disabled. Based upon that knowledge, re-enable all but one half of the
set of files you know contains the culprit. Restart and test.

Continue this narrowing down of the possible culprits until you discover
which item is responsible. But remember, this test is only needed if the
problem was cured by disabling startup items. If startup items aren't
responsible, and you yourself aren't launching something that then stays
resident and polls the internet, then the most likely culprit is malicious
software and you need to install and use the proper scanners to get rid of
it.