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After following and completing these guides: MagSafe DC-In Board, and Battery Replacement, and allowing the battery to charge (which it did), I started up the laptop. Everything seemed to be working normally for a few minutes, until I noticed issues trying to open and run just about anything. Finder works, but anytime I try opening a file, it says “You can’t open the application ______ because it may be damaged or incomplete.” Strange thing was that I was able to use a couple apps for a few minutes, but after some time had passed, they would not open again. Even apps such as Activity Monitor and System Preferences respond the same way. I fear I may have damaged something while removing and putting back the logic board. Any advice is welcome. Update (07/28/2022) This fixed the problem (so far!): https://techwiser.com/fixed-macos-error-

It sounds like you need to replace the HD SATA cable as it may have been damaged during the repair. Here’s the needed part MacBook Pro 13" Unibody (Mid 2012) Hard Drive Cable and the guide to put it in MacBook Pro 13" Unibody Mid 2012 Hard Drive Cable Replacement Here’s a bit more on why you need a cable and a strip of electricians tape to help protect it Your Hard Drive Cable Is A Ticking Time Bomb Also becareful with the bending of the cable, many people damage the cable by creasing it at the locations where the cable needed to alter its direction. When you crease it you damaging the foil wires within the ribbon cable. I use an old BIC pen ink straw as a forming brake to help retain the needed radius of the cable so its not a sharp bend.