It is quite likely that is is a program you have installed that is in your "Start up" directory ( i.e. it loads automatically when the machine boots up ) and is looking for a web connection.
Try and work out which program it is, and go into it's settings and stop it from trying to connect of it's own accord.
Or you could remove it from the Start Up folder so that it stops loading on boot up altogether.
Or it could be the "Windows Login" thingy, which is a pain in the bum, and is to do with having more than one user to a PC so it can save personal settings. Go to the Microsoft website and see if you can find a solution in their Tech net section.
Hope the above helps
Bingo
P.S. Sometimes Windows 95 gets itself in a right pickle, and the way forward is to do a nice clean rebuild. The other option is to upgrade to Windows ME, which is quantum leaps better than Win 95 ( and 98 ) a lot more stable, and more user controllable.
[ 25 September 2001: Message edited by: markbingo ]