I went and got the computer, paying my $60 (which, if we need to take it back in for the same issue will not be charged again and we would go to the front of the line - the shop seems like a good place), came home where we plugged it in and...yup, started up just fine. That was both a relief and a concern. What was wrong?
Anthony promptly started surfing and after a few minutes, it froze up, just like it had done to him on the Friday this all started. And, yes, we tried multiple times to boot it up. However, I wasn't part of that, so I don't know it it was ever given time to rest between tries, which can make a difference.
Oh, and I should mention that the computer wouldn't start up when we got back from Colorado, either. Later, Anthony tried and was able to boot it up...then this happened Friday night.
Anyway, we manually shut it down, I suggested time to rest, then tried again to boot it up. It came up fine in safe mode and then in regular mode. As Anthony had been using Chrome with things went awry, I suggested using a different browser and we did...for a while. I see we're using Chrome again, but so far, it hasn't happened again. Go figure.
I'm glad that we've got all of our data, but I wish the problem had been really solved.