The internet keep booting up when I am off-line doing other things, for example.
burning an audio CD and a few other things.

Hi bencat,

If I understand your question, this should solve it. Go to -

Start / Settings / Control Panel / Internet Options / Connections

Highlight the dial-up setting you use to connect to the internet.

Tick off "Never Dial a Connection". 

Click "Apply". Click "OK".

This should stop your computer from dialing-up automatically. If you
have any questions or if I misunderstood your question, please post a
clarification before rating my answer. Be sure to include  your OS
(Windows 98 or?) and your browser (Netscape or?).

Thank you,
hummer

Your solution to my problem was right-on. THANK YOU.

Hello again bencat,

Great news, thanks for the update - I was fairly certain it would work
because we've experienced the same problem (I know how annoying it can
be!). Thank you also for your thank you and nice tip, both are
appreciated.

Sincerely,
hummer