Since I've been fighting a lot with my Asus Pad Infinity TF700T for the last couple of weeks, dealing with the driver installation failure I finally found a solution from an article about MTP issues on a Xperia smart phone that I thought I could share.
The first billion of search results on Google gives you the advice to install the Microsoft MTP Porting Kit, which I tried, and I also tried to install the ASUS Sync suite from Asus Download Center but nothing seemed to help. I know a lot of people have been fighting with the same issues and the solution I found was annoying and easy. The solutions follows:
Settings > Apps > All
Make sure Media Storage isn't disabled - for some unexplainable reason mine was.
Other ways to solve issues with the same symptoms (driver installation failure, code 10 - fail to start device etc.) might be solved by simply clearing the cache for an app called MTP extension service (this is an app that is not included in all Android devices). Also make sure USB Debugging Mode isn't enabled under Settings > Developer Options.