Do you have any networking components installed? That is, Dial-Up-Networking to an ISP or a network card?
Windows 95 stores passwords in a password list (*.pwl) file for each user that logs onto the machine. Logon is normally only available if you have networking installed. A way round it is to install dial-up networking (even if you DON'T connect to the internet. In the Networking section of the Control Panel, make sure one of the protocols you have installed is Microsoft NetBEUI and that you have Client for Microsoft Networks installed. Using regedit to examine the registry, search for 'autolog'...it will find an entry called AutoLogOn....if the value is set to 0, change it to 1. This will cause Windows to prompt for a user name and password at every boot. Having 'logged on', Windows will now store all the passwords, inclusing the screensaver password, in the appropriate *.pwl file.
Note, hitting the 'Esc' key at logon will log windows on with no user data, so any passwords will be bypassed.