First of all, uninstall the printer drivers that caused this problem to begin with. Once you have done that, restart your laptop and verify that the tiles work. Give me your results before we continue to troubleshoot!
NOTE: The Start screen containing the tiles does NOT require a touchscreen to function. I am using Windows 8.1 Pro on both my main gaming system (see my sig below) and on my Alienware 18 gaming laptop; both do not have touchscreen capability. The Start screen and all the tiles work perfectly on both systems.
**UPDATE**
I just read about this same exact problem in another forum. Ultimately, the fix was that the user had to create a second admin account and the tiles worked for that login. This was due to the fact that part of the registry had been damaged by installing another program. He did have to transfer all of his documents over from his old account to the new one. But, it did work and his Start menu tiles work just fine now using his new account. He deleted his old admin account once he had backed up all of the data from that account. If you want to be safe, you can keep the old account until you have verified you don't need access to it any longer.