Dropped Switch Lite, stuck on blue screen...HELP!

To confirm, when you said you turned it off and on, do you mean a hard reset? If that's the case then instead try the following:

http://en-americas-support.nintendo.com/app/answers/detail/a_id/22347/~/how-to-initialize-nintendo-switch-without-deleting-save-data

If that displays anything then just power off again without selecting anything (be careful on that screen as you don't want to delete anything!). At least you then know that the Switch is partially working.

What happens when you plug it into the dock? Does the green dock light illuminate? If so, try leaving it in the dock for about 30 minutes or so as perhaps the battery has fully discharged.

/r/NintendoSwitch Thread