Hi, All you have to do is hold the power button until it shows the apple logo. It is unnecessary to hold the home button unless you are hard reseting. I can tell this probably didn't work either, so here's a suggestion: If you didn't try this yet, try a different lighting cable or try cleaning the one you have. If it's dirty then the dirt may be blocking the way. If it's the cable itself, then it won't work on any other iPhones you have. I don't know what to say except to replace the battery or call Apple to fix it for you. This has always worked for me. I hope that this will help you!

You should probably look online for a replacement 72-pin connecter. If something is loose or broken it could make the cartridge fit on looser (perhaps from loss of pins.)