MacBook Pro asks for update on startup and hangs up

Trying to help my son who lives away from home and has a MacBook Pro with Yosemite. Suddenly started asking for an update on startup saying "The user graphics resource appears to be invalid" and asks for password. Accepts password then goes to a white screen and nothing happens.
Unable to boot into safe mode, verbose mode, or recovery mode. He doesn't have another drive to boot from right now.
Any other ideas to get it started?

It may be a hardware problem. You didn't give us any specifics about his MacBook Pro or which version of OS X it's running. However, from the sound of the error, it may be time to take it to an Apple store genius and have them run diagnostics on it. The diagnostics testing is free if he takes it to an Apple store. If the graphics adapter on his MacBook Pro has failed, the machine will display the symptoms you described. It may be something else though which is why it's a good idea to have Apple check it out.

There are all kinds of hits with a google search on variations of 'mac user Graphics resources invalid', and an amazing number with almost word for word posts from way back.

One general theme seems to be something messed up with FileVault.

Maybe even try un-encrypting the drive or do some other reading on topics like this:
login - What does "[Update Needed]" mean when attempting to boot from an encrypted backup? - Ask Different

Yes, he is booked in to an Apple store for Tuesday but trying to sort it out for him before then.

I have seen a number of the posts in other fora about the file vault issue. Problem is we cannot get the thing started to get in and change it despite all of the various methods suggested.