Are you attached to a network as sometimes the square doesn't appear if you aren't. Have you tried a restart?
what make/model laptop do you have? do you know the button to use to access bios as often you can hold it down before you start laptop to force way into bios.
if you can get installer booting, run a start up repair and see if that fixes it
change boot order so USB is first, hdd second
boot from installer
on screen after languages, choose repair this pc, not install.
choose troubleshoot
choose advanced
choose start up repair - this will scan PC and maybe fix this - will ask for logon info
if that doesn't help, you can use this to copy anything off C drive you want to keep off laptop: http://www.howtogeek.com/howto/windows-vista/use-ubuntu-live-cd-to-backup-files-from-your-dead-windows-computer/
I would suggest a Reset IT only touches C drive and basically sets windows to brand new. The problem with this error is I don't know if it is your user playing up or a windows function that doesn't load the screen.
If it is just the screen, then doing a reset and keeping all your files (everything in library folders (like music, documents, pictures, movies, etc)) and settings (including logins) is the best approach. If it is your user, you will need to wipe everything.
I would keep files and settings and see how that goes.
to get to reset,
boot from installer
on screen after languages, choose repair this pc, not install.
choose troubleshoot
choose reset this PC
make your choices and then PC will restart and reinstall win 10.