IPhone 5 won't turn on
So this past few days my phone battery percentage is acting weird like stuck. My battery percentage shows 51% for 2 hours, so I force open it (home&sleep button) then the battery shows 12% a few minutes then the screen gets glitchy and it restarting itself again and the battery shows 3% !! It keeps restarting itself for 5-6 times and the battery also changed. Today my battery shows 3% even when I charged for an hour it still won't increase/decrease so I decided not to charge jd just use it until the phone suddenly dies (maybe the battery is died) then I connect it to charger and the phone turn on itself showing the battery at 1% And it charges for 10 minutes and the battery stays at 1% so I force close again (home & sleep button) and it shows 100% so I just left it there to charge when I came back my phone is showing the apple logo for 2 seconds and it turn off and shows the logo again and fade shows the logo and fade. It keeps repeating so many times! When I unplugged it from charger, the phone just completely turn off and won't turn on at all even when I force open it. It only turn on when I plugged the charger and it just show the logo then fade and show again and fade that'so all. I tried to connect to iTunes but itunes doesn't even detect the cable at all as if I haven't plugged any cable to the computer. Now I just plugged my phone to the charger and that logo fading thing is keep repeating for half an hour already Pleaseeeee help me... Anyone?
iPhone 5, iOS 7.0.4