SOLVED!

The problem was that /system/osso/dsm/display/inhibit_blank_mode GConf value was invalid. It had value 3 (Inhibit dimming/blanking) instead of the valid value 0 (No display blanking inhibit).

So the fix was to run this command in terminal:
I guess using GConfik app works too but it seemed to change the type of the property from Int to String (so I guess terminal command is safer).

The solution was found by googling what each relevant "display" gconf property meant and this came up: http://www.gossamer-threads.com/list...rs/61201#61201