You could always try the hibernate mode. Once in hibernate the computer does not use any power. My netbook will restore from hibernate in 30 seconds and is in the same situation (all programmes running) as I left it when I set it into hibernation.
if you decide to set your laptop to hibernate, is that the time before hibernation must always be less than your battery life time if you use the machine on battery power. Otherwise the computer will drain before the hibernation can switch in.
If you tend to leave your computer unused for long periods hibernation can be useful, otherwise it's probably best to select the stand-by mode. You can of course select both - putting the computer into stand by if it's not used for say, half an hour, and then into hibernation after another hour. You certainly wouldn't want to keep the machine on stand by for more than a couple of hours anyway - there's a risk of losing any unsaved data if the power supply failed for some reason.
I don't know my laptop very well do I? I have just found that if I press 'Fn' key and F6 the screen shuts off with just a hint of the display, and comes back with a key touch as you say Peter. It's an Acer - I haven't seen an Fn key before.