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One of the issues upgrading to a SSD is the data rate thru the SATA cable is higher. If you have the older cable it will often respond like this. In addition the rough aluminum surface of the uppercase wears the cable. I strongly recommend you apply a strip of electricians tape on the uppercase where the cable crosses over. In addition, don’t fold the cable with tight creases! Your want round arcs at the corners. Here’s the better cable MacBook Pro 13" Unibody (Mid 2012) Hard Drive Cable (Yes, this is the 2012 systems cable) and here’s the IFIXIT guide you’ll need to follow MacBook Pro 13" Unibody Early 2011 Hard Drive Cable Replacement
I think what they meant when they said to replace the SATA cable is to replace the Hard Drive/Solid State Drive cable. If so it’s super easy and also inexpensive to do so. You need a working SATA cable in order to run your OS fine and if you have a damaged or defective one your SSD/HD cannot be properly read. This “confuses” the Logic Board therefore making it impossible to use the computer. Replacement HD/SSD Cable Tutorial on how to replace it