Chosen Solution
My iPhone 6 is showing a voltage rise when tested through a multimeter when connected to power, but the screen will not turn on and the phone shows no other signs of life, such as vibration motor, sounds, etc. EDIT: I did just find now that the battery is not charging past 2.56 volts, even with a new dock connector. EDIT 2: I just figured out that there is a quiet ticking noise inside the phone when charging, leading me to believe there is a short.
Is your phone detected by an iTunes enabled computer? If you shine a bright flashlight on the screen, do you see a dim image? If you have access to a USB Ammeter, you could use that to determine if the phone is really drawing current when it says it’s charging. If your battery is maxing out, it could either be due to a dying battery or a problem with the charging circuit. the easiest thing to try is a replacement battery. You can follow this guide for the replacement.