Can not erase my Mac OS X base system
I agree with Steve Chambers. Your hard drive is likely dying or dead (google "click of death hard drive"). An authorized Apple repair center can swap it out for a new drive (get an SSD, it'll speed your machine up), or you can DIY. I don't know your exact computer model, but the most recent Mac laptops that shipped with spinning hard drives were around 2012, so here is an example of how to replace your hard drive with an SSD (assuming it's a 2012 Macbook Pro, for instance): 
https://www.ifixit.com/Guide/MacBook+Pro+13-Inch+Unibody+Mid+2012+Hard+Drive+Replacement/10378

It's actually quite easy to do yourself if you're careful and order one of the upgrade kits with the appropriate tools (small screwdriver and a T6 torx) along with the SSD. 

Good luck! Cheers,
-joe