You have have turned on some crazy option (probably by pressing random buttons or alt or ctrl combos).

The fastest way to resolve this and show it's not a system of installation problem is go to you documents folder and delete the maya folder. Please do not have maya running. Then the next time you start maya it will create a new folder named maya with default preferences.

To turn of interactive creation go to the mesh menu and you will see a check box for interactive creation just uncheck it. There will also be a checkbox in the surfaces menu.

Once you have deleted the documents>maya folder and re-launched maya. You will get the startup dialogue (just close it). Then before you do anything! Before you press any keys. Create a poly primitive and see if you can select it.

Do not be to discouraged I have inadvertently gotten maya in some odd states. You get modeling and into a rhythm and then press some odd key combo and the next thing you know maya is acting all goofy. This is why once I have a good shelf and gui setup I make a copy on my maya folder and if maya goes bonkers I just replace the maya folder with the copy. It is much easier to replace the folder then spend days trying to figure out what magic key combination you hit to get maya all messed up.