I'm thinking I should maybe just give up on the whole computer thing; this is ridiculous.
Went to print something a few minutes ago, and nothing happened for a while until eventually the printer popped up a dialog box on the screen saying that the printer wasn't responding.
Tried to update the drivers, and when the driver installer went to find the printer on the network, it couldn't. The printer does, however, show up under 'Printers' in the Control Panel.
It's a Canon MG5250. Pretty much brand new. Still haven't got through the set of replacement ink cartridges that came with it.