My phone says that I m out of battery, yet it s fully charged?

I have a samsung galaxy s3 which I ve had for about 3 years now. (I assume that I have to get a new phone because of this problem…) There are no cracks on my phone but there are scratches. There has been problems with my phone before in which my phone didn t turn on and I had to plug it in first then put the batter in to work. I ended up getting a new battery. However this time, my phone was working normally up until it froze, which isn t too abnormal, and was overheating. I waited a moment to see if it would unfreeze and then took my battery out, putting it back in after a minute. It didn t turn on, tried again, did not work. I tried to do this with a spare battery, same thing. After about half an hour of trying, the screen popped up an empty battery which I thought was weird because it was full before. I shrugged it off a bit and plugged it into my charger. Then a few minutes later the battery popped up saying it was full. (the picture of the battery pops up when off) Cautiously, I turned it on and shows me the samsung logo, and so on, turns off. Eventually it works and my phone is ready to use but it turns off and does the same thing again in about in hour or so. I ve searched answers before and some say I need a new part for my phone, etc. However I ve spent so much money on batteries and other things (the audio jack is also not really working) that I think it s time for a new phone. I just need to see if fixing it will be costly. Thank you for reading!

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