Can't boot up Windows because you're getting a BlueScreenofDeath?
Same for safe mode?
Only hope seems to be recovery mode but it's giving you errors and your only hope seems to be a clean install?
And this is a laptop where you can't simply pop out the hard drive to back everything up?
Well you're in luck. All you need are a large external HDD (hard drive) (large enough to hold all your files) and an admin account's password.
Step 1; boot up the computer normally, let it crash (blue-screen) and auto-reboot
Step 2; it should go into 'start-up repair' automatically
Step 3; cancel the 'start-up repair' utility and continue till you see a pair of blue links, the lower of which says 'advanced recovery options'; click it
Step 4; you will need an admin password here; select an admin account and enter the password
Step 5; select 'command prompt' and then plug in your external hard drive
Step 6; type in 'regedit' into the command prompt window
Step 7; in the regedit window, go to File->Export
Step 8; at the bottom, there should be a drop down list with an option 'all files' (its right below the text field where you specify the save-name of the registry dump)
Step 9; you've now got a passable set of explorer's functions! (don't bother trying to start up the real explorer, as it won't be able to access System32.dll in recovery mode) - you can now copy+paste files/folders from your bricked computer onto the external hard drive! (One file/folder at a time, I know, but way better than nothing!)