Often , by inadvertedly hitting the wrong keys, my modem gets
connected to the phone and I cannot hang up and restart the internet
unless I shut off the computer and reconnect. If anybody knows of a
better way to hang up please let me know.

You should be able to see two small computers in the system tray (this
is at the bottom-right of your monitor screen, where the time
appears). Right-click those two computers, and hit DISCONNECT. If that
does not work for you, then perhaps we'll need to know who your
Internet Service Provider is.

If there is an error in your Win98 and you cannot see or use the
connection icon in the task bar to disconnect. Maybe you could unplug
the phone cord from the back of your computer to disconnect. Its been
awhile since I have used dial-up, so this is just a suggestion.
Good-luck :)

Try uninstalling the modem and restart the machine before installing
it again and check your Internet Explorer setting option Connection
and don't set your dial up to be default connection whenver u need
then connect it..
play safe.. 
have a good day
thanks
sanjay

You might also want to download a program called Spybot - Search and
Destroy, it will scan your computer for any spyware and remove it. 
Some spyware uses your modem to auto dial a long distance number with
high minute charges, most being porn numbers that get their money off
the people who don't even know the modem is connected and recieve
charges.  Play safe, not sorry.  Oh, FYI, spyware slows your speed
down and moniters your activities and many times emailing these
activities back to the mother company for their personal use.

in 98 - hit ctrl-alt-del, look for a 'rnaapp'. most likely it's
running. end it and that should free up your modem.