I attempted to install the update for Leopard but they said I didn't have enough disc space and that I should remove some of the stuff on my start up drive. I'm sure you know what that means, but I don't!
Yes, your disk is too full. It should never be more than 80% full and 50% is better. Too many iTunes songs or iPhoto pictures? Something is filling it up. Open the main HD window in list view, then go to View Options and check the box for Calculate All Sizes. Open up subcategories by clicking the little triangle to the left of each folder name. It will take a while but it will calculate the contents of each folder. Don't delete stuff you don't understand (like the Library) but if you find the culprit to be too many movies, pictures or iTunes, delete or archive somewhere else. Then you should be able to upgrade.