I know Dora has probably either found the answer or never thinks to look here anymore. I've had this problem three times over the past 5 years, and I knew the answers above were total red herrings. Mouse drivers indeed. None of these experts knew the answer, so answered completely different questions to try and sound knowledgable when they are not.
It's nothing to do with mouse drivers. If you can double-click an icon (or other screen object) successfully, then there is nothing wrong with the mouse drivers and nothing wrong with the double-click speed settings, etc.
It was obvious from the OP that she could double-click successfully, but the computer would not always 'listen' to the launch command associated with the double-click event.
I've tried many things and only today found the solution just by chance. If you go to Control Panel > Add or Remove Programs > Set Program Access and Defaults, usually you will find the configuration is 'Custom', yet under there everything is set to use your default program. If it is, just set it back to 'Microsoft Windows' and click 'OK'. You'll immediately see all windows and icons blink a couple of times, then hey presto - and also, if you found your computer had been inexplicably slow for a long time just to do very basic things, it seems this will fix it.