psugar raises some good points. Your installed version of DirectX may be earlier than the one required for SoaSE. This would definitely affect the cursor video problem you are having.
I'm only guessing here, however, sre you using transparencies on your desktop at all? If so I'd recommend that you disable them to see if this solves your problem in this game.
Also, this can be a problem with decreased (video) hardware acceleration - I'd suggest you try turning that up to max. From my experience you will inevitably get cursor problems unless it is set to 100% on some video cards.
You might also look at decreasing the video options/settings in the game to see if your cursor re-appears.
Some games have an option for "hardware cursor" that you can turn off and on. Although I've never seen that specific option inside SoaSE, that doesn't mean it isn't there, I could have just overlooked it. However, if it is there, I'd try that too.
Have you tried running the game in "windowed" mode? Or, if you are running in windowed mode, have you tried turning it off? It sounds like your cursor is actually there... beings as the click places highlight and your cursor shows, but it's "behind" the video layer on your screen when displaying the game, when it's not over something that's able to be clicked.
Just a thought or two...