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This little trick will allow you access to control panel, CMD, Access to the C:\ drive and youtube should be unblocked or most websites depending on your schools filter system.
Simply press the power button to start up the computer, press F8 when the computer starts booting, now you should have a black screen with some options.
Choose "Directory Service Restore Mode" or something similar to that; it will take a few seconds to load, dont get scared it has frozen as sometimes it can take longer than usual. Your ordinary school login screen (if you have one) should pop-up, as your networkiing is still enabled you will be able to log in with ease, it may take longer to log in than usual but I guarentee you it will login.
Once you have logged in it seem as though your school laptop/computer is ordinary and un-restricted.
I have not done things like this in a while and my CMD skills have been forgotten... so you can use CMD

but the only probelm I had run into was when tryng to alter some files it asked for Administrator password. This should be an easy fix to removing restrictions (also Directory Restore Mode; I chose as Safe Mode with Networking is usually zoomed in and may catch the attention of various teachers / school students... but on D.S.R.M it displays as usual. Hope you benefitted from this and i could not find anything as quick as this, I read one which showed how to using Startup Repair or something similar but this included waiting 10-40 minutes...and it had the same outcome as removing restrictions. Your Welcome