The Mac does not shut down when the cable modem goes out. You obviously had something else going on there, that you have not mentioned, at the same time as the cable outage.

It should not be necessary to reboot after the cable modem comes back on again if the computer is in a usable state. Yours had something else going on. It is not normal practice to require a reboot once network connectivity is restored. I guess that something locked up the ethernet port, and everything else, when the cable went out. When the cable modem shuts down nicely, it has the same effect as you pulling the ethernet cord from the computer. No effect whatsoever. Modem back and the Mac establishes the network like again.

Pushing the power button does nothing. Pressing and holding for at least 5 seconds will shut it down.

Glad you got the the all-in-one sorted out. The printer must have been installed for you to have printed with it. It was probably using the GIMP drivers if you had not installed any software for it.
Either way, you're back in business

P