MacBook Pro 13" Mid 2010 is not seeing internal SATA HDD
You may want to take a look at this answer to a very similar problem affecting 2012 13" MBPs. It's highly unlikely it's your SATA controller - if your MacBook can read DVDs or CDs then it's definitely not your controller as it's the same one that the HDD/SSD will be connected to (Intel Series 7 Platform Controller Hub).

As for why these cables fail I've yet to get to the bottom of the issue, but the ones I've replaced have no visible mechanical damage whatsoever, and replacing them has restored full SATA functionality.

The question/answer I linked to has some information that may make your cable change slightly easier.