TomGeorge:
Hi Paul, some LCD monitors die because of the power supply to the rear light system failing.
You can check by turning the monitor on and with some input that you know should be displayed, look at the monitor surface from the side while shining a torch on it.
I know. 
There is a firm in Sydney who actually repairs monitors, strange thought that be. The fellow turns up to the North Rocks markets, perhaps less regularly than he used to. Some years ago, I bought a second-hand monitor from him (I mostly buy second-hand monitors - and computers - much cheaper that way) which failed - the backlight - with a bad smell. I took it back to the markets and he said "no trouble - we will fix it"! I was somewhat shocked - who repairs monitors these days? Nevertheless, my son picked it up later from them in the backblocks round Auburn and it proceeded to work just fine. (Replaced the inverter.) I forget now just which one it was of course.
TomGeorge:
If you can see the image then the backlight or its supply is u/s.
And you can get replacements on the tadaaaaa...internet , wow isn't electronics wonderful.
One monitor here - of the said many - is documented on the 'net to simply require replacement of the electrolytics - perhaps $10 from Jaycar. The problem is - I pick up monitors at garage sales for less than that though the 24" I am presently using did cost all of that. So that's the situation, I am just a little reluctant to trash the older ones until I have spent the time to conclusively determine they are BER (in the "experimenter" sense).