Frankly speaking, I don't have an idea.
Did you do any recent change which might of influence? Install some Internet-related program? Then try to undo it. A scanreg /restore to the situation five days ago might help (albeit in a very crude way).
Then run all 5 of Bob Proffit's anti parasite suite. A parasite could well be the cause of the problems, I think. See: http://reviews.cnet.com/5208-6132-0.html?forumID=32&threadID=1313&start=0 for the programs involved. Do this even if the scanreg /restore helped. It doesn't remove the parasites, they're just no longer activated, but still present.
The last resort would be:
(1) A reinstall of Windows 98, or
(2) Change to adsl or cable internet, which doesn't dial up connection. But of course, depending on the deeper cause of the problem, it's not guaranteed to be trouble free in your situation.
Here in Holland, adsl is rapidly becoming cheaper. You can get it (512 kb/sec or more) for less then 1 USD a day (which is equivalent to about 40 minutes dial-up a day for a 'free' provider). With 2 children and MSN and online gaming it has become an easy choice.
Kees
Win98se
When I go online, and just after the online icon appears on the task bar, a pop-up, headed -Explorer- appears with the message This program has performed an illegal operation and will be shut down. if the problem persists, contact your program vendor.
It causes no trouble other than the fact that when I click it off the on-line icon and other icons disappear from the tool bar.
I used to have a connect light on the keyboard, but that no longer works, so now I forget if I am on line or not. I can get over the problem by tucking the pop-up out of sight and deleting it after I have gone off line, but that is a pain.
Any ideas how I can prevent this from occurring.
thanks for any help.

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic