about the ubuntu logo:
yes, obviously something happened, we are aware of that. most probably plymouth stopped working and revealed the "layer underneath". i don't know.
you answered one of many questions by providing the lspci output.
it looks like you have the right graphic driver for your card, and it is running, too.
of course you should do some research, preferably on linuxmint forums, then various ubuntu forums, then the web.
you could also try switching to the open source nouveau driver, to see if that fixes your problem, but i'd rather you would answer all questions and suggestions made so far to your best knowledge and ability.
the graphics angle is based on mere guesses right now.
plus one more question:
do you remember when the problem started happening, and something you did before that? maybe install a new application, did an update/grade, some such? anything?