I would have though that the only time you get a "blue screen" is if during installation, you have somehow bypassed "adding a user".
Mandrake, by default doesn't show root as a user on the log in screen (though I'm not quite sure why you are getting a blue screen, without a blank login dialogue box).
I am presuming that you could try one of the other options at boot (again presuming that you are offered them by lilo) of either "linux - nonfb" or "failsafe". See if they offer you an option to start the "runlevel" at 3 (like dos) as opposed to 5 (graphic i.e. kde, gnome, etc etc) you could (I think) then try "startx", and see where that gets you.
If like me, you are often in the dark as to how it works under linux (and have plenty of time), just re-install. This is not always the prefered route that the knowledgable type like (but they also know what do do and where to go - file wise). But as you managed to install it in the first place, just follow the same route, but change anything that you know was "wrong" the first time.
If you do re-install, if mandrake asks you something, to prevent confusion, try to apply what they are asking you i.e. when it wants a root password - then to start with, just use "rootpassword" - you can always change it later. If it asks you about where to install, pick the "use existing partitions" option. For a user, just use stuff like "me" and "mypassword", again you can always change it later.
For your mouse, as you proceed through the install - the default would be something generic like "ps2wheel mouse" or somesuch, it should have a dialogue and then you would have to select "USB Microsoft intellimouse" or maybe just usb or microsoft intellimouse "radio button" - it should then offer you a little "test your mouse screen" where you click the buttons that it asks you.
Post up what happens. And IMO, don't bin windows, just dual boot it, and use linux - then at least if like me, you have lots of disasters to start with, then at least you can boot back into windows to get online assistance and post here!