2011 macbook pro not responding to startup commands
Since the shift key or option key should be recognized by the system well before the Apple logo arrives, you can conclude that you have a failed keyboard.

Plugging in any USB keyboard and booting in safe mode (shift) or single user mode (command s) should let you know if the keyboard has issues.

Now the Apple and blue screen are good. They mean that the core OS and hardware are fine and that the start process is hung starting your user. My guess is you need to boot to internet recovery (or an external drive) and then repair some damage to the user files or the drive itself. Then you can delete the .AppleSetupDone file and make a new admin account to see if the Mac can work.