"How do you Solve Service Battery Warning"に関する回答Try taking it to an AASP (Apple Authorized Service Provider) and have them run a battery test on it to see if it is failed prematurely or if it's just exhausted.
"Can I get "certified" to fix my Macs without voiding their warranty?"に関する回答Certification has no meaning unless employed by Apple (as a Genius) or an Apple Authorized Service Provider. The only thing it does it you aren't, is provide a way to differentiate yourself from another candidate should you choose to pursue a job at one of these locations.
"Replacing the video synchronisation cable"に関する回答Apple's part number for the VSYNC cable for this model is 922-9161, hope this helps. Chris