This is a very odd issue
Have you tested booting the console up with no controller attached and no cart or game inserted?
Can you even back out of the Memory Manager?
Not sure if there is a way to boot directly into the Memory Manager with a Joypad combo or other trick, yet so far pulling up blanks on searching but there may be a way to do that and maybe that is what is happening, will keep digging though...
You may need to clean your pad or get a new one, I would just clean itBy holding the left or right trigger when turning the system on, you can access the memory manager.