Not charging or powering on
When I plug my phone in, it shows the charging icon, the it disapers and vibrates, then it shows up... over and over. When I hold the power button it shows the Samsung logo, then just shuts off.
If you have not done so, I would suggest trying another battery. From your description it sounds like a failing battery. The battery at this point may be only capable of supplying enough power to turn the phone on but does not have enough power to boot up the phone. It takes a higher voltage to boot the operating system than it does to switch on the phone. So you may consider replacing the battery first to see if it fixes the issue.