MB Air freezes on "Cosmos" screen during power-up. Is there a "safe mode."

I actually have three interrelated problems with my 4 1/2 year old MacBook Air: the clamshell hinge broke 2 weeks ago (and apparently Apple has a program to replace this defective part), yesterday my display went "gray," and when I hook up an external display and power-up only the start-up picture of the cosmos is seen. Any idea what's happening, and can I get the machine to function?