Today I really needed it so I bought a new VGA cable and the problem persists. When the monitor isn't connected to a computer, the menu screen is perfectly rendered, so there's no problem with the panel itself. I have cleaned the monitor a couple of times since it was last used and the cloth could have been less damp, so I can't completely rule out water damage. 

The only thing I can think of doing is to open it up and check around the connector to see if anything's loose on the inside. If there was a problem with the panel itself then the menu wouldn't work. The worry is it could be something that interfaces between the PC and the panel that's causing the lines, but it looks like a distinctly analog fault, a lot like a TV arial not plugged all the way in. There's a small chance the same might be true of the other end (the laptop VGA output)! I'm not keen on getting inside either of those areas but it may have to be done.

Oh the other thing is there seems to be a white 'blowout' like someone turned the contrast and brightness way up even though they're on average setting (and turning them down doesn't really help it just makes it look dimmer and lower contrast but still blown out)

Going to try: loose connections, dust out, crossed wires.

I had loads of problems with a recent Windows 10 update, that updated my graphics card driver and made it 'obsolete' - I did think the inbuilt graphics card had toasted itself, but found the old driver, re-installed and so far (touch wood) its been OK.

Just something to possibly think about? 

It's either the VGA out on the laptop or a graphic driver issue as suggested - I do have a fuzzy memory about graphic driver issues leading to issues like this with external displays (too much strain on the compromised hardware to deliver two displays at once so the second one craps out) so that's the next thing to check.

Although to be fair it was a pretty thin plot to begin with so that's not saying much.

Installed a new driver and that didn't help. I tried switching to only display on the affected screen and that didn't help either BUT I did notice something curious - First of all it's literally impossible to change the resolution of the affected screen, or the orientation, these options are simply blanked out. Secondly the brightness slider, though it lets me move it, doesn't affect the brightness of the screen at all (which as mentioned is exceedingly bright as it is - looks like 100% might look like.

These issues are not replicated on the other laptop.

For the issue I had, I really thought the graphics card had died which would have meant new laptop time, it was only a good few days googling that I found the answer (and legacy driver).