Do you have to reboot or will just closing then reopening IE/OE work?
MUST REBOOT
If closing/reopening does not work: do you have to reboot or will Logging off/on Windows work?
LOGOFF DOESN'T WORK
How do you know that "
the computer goes online via my ISP ..."
THE COMPUTER HANDSHAKES WITH ISP AND TELLS ME I AM CONNECTED (I AM ON DIALUP)
Is the connection seen as connected? What happens if you disconnect the reconnect here?
YES. RECONNECT DOES NOT SOLVE NEED TO REBOOT
Also what Power Settings do you have? Do you have Standby or Hibernate on? Or what?
I'M NOT SURE (NOT AT COMPUTER AT THE MOMENT) BUT I THINK BOTH. (IE NOTEBOOK SCREEN GOES BLANK AFET ABOUT 10 MINUTES AND THEN OFF SOME TIME LATER)
Lastly

Is this a new problem? Were things working OK previously?
I'VE ALWAYS HAD THIS PROBLEM
What is your connection? DSL?