......the computer seems to come back to life but the display doesn't. If I investigate, a box comes up telling me that the monitor isn't getting a signal from the computer, followed by another box saying the monitor is entering powersave mode.

I have had the same problem but well before the recent Windows update.

In my case, it could happen as I was using it, not just on waking it up. If I re-booted straight away, the problem often re-occurred. If I left it to cool down before rebooting, the problem went away, at least for a while.

One of the cooling fans started catching on start-up and it sounded like the computer was spitting out nuts and bolts. When I opened it up for inspection, the inside was full of dust and some of the holes in the casing were blocked. I removed the dust with a vacuum cleaner and haven't had the blank screen problem since.

It could be that your computer is overheating and the Windows update is just a co-incidence.

DC