The game uses the N64 Controller Pak (Mem Pak) for saving games. I assume that the white crystals do nothing if you don't have the Controller Pak. Did you get a Controller Pak message when you started the game. Anyway, how about pressing the Right C button when you're at the crystal (which is the universal action button in this game). Does that work?
If all else fails, you can always use savestates, but I would realy solely on those if I were you.
P.S. If I read correctly, you are using a Logitech Sidewinder gamepad. Is this the very first model or some newer one? Because if it's the first model, it does not have enough buttons for N64 games.