administrator v new user

immediately after purchase, i set up an internet
connection and then ran my windows xp prof laptop in it's
administrator mode with an allocated password - all went
well so far.

then, following the on screen instructions [or so i
thought] i tried to add other users, first naming an
administrator and then another family member as an
additional user.

each time i complete this procedure i am told that i have
lost my internet connection and the desk top icon for my
isp disappears.

can anyone tell me what i am doing wrong and how to do it
right?

i want to set up my comp for two users with the same isp
internet connection and administrator status available to
both but for each person to have a personal password.

dave