My Iphone 4 won't activate despite putting in the correct apple ID?

I've had my old iphone 4 sitting in a drawer for years and I decided that I want to switch back from my samsung mini s3 and start using my iphone again. I remember wiping my iphone a few years ago via itunes or something like that and restored the phone back to its origional settings. Now almost 2 years later the iphone isn't letting me activate it. So far I have chosen the country and language settings and connected it to my Wi-Fi I'm stuck on the "Activate iPhone" page. It's asking me to put in my Apple ID and password yet every time I put it in it tries to connect for about 5 seconds and then tells me that it's incorrect however, I know for definite that what I'm typing in is correct as when I log into my apple ID/itunes on my laptop it works and logs in. I don't understand why it keeps telling me that my apple id is incorrect even though it's the only one I have ever used on that phone. How do I resolve this problem and get the phone to activate?
(I don't think I would be able to take the phone into an Apple store because as I have said it's been sitting in a drawer unused for a couple of years and I think that all of the packaging has been thrown away therefore there would be no way for me to prove to them in the store that the phone is actually mine)

What do I do? Thanks in advance.

Added (1). * I have just pressed the "Activate Help" option and it says "Your iphone could not be activated because the activation server can't be reached. Try connecting your iphone to itunes to activate it, or try again in a few minutes" - I have tried connecting it to itunes yet it still isn't working?!

WHY IS MY IPHONE 5S SUDDENLY OVERHEATING AND DRAINING BATTERY FAST?

WHY IS MY IPHONE 5S SUDDENLY OVERHEATING AND DRAINING BATTERY FAST? - 1

Added (1). Okay. I'm sorry for caps lock, didn't mean to.
But I got my 5S last July, which is not so long ago. But then, out of the blue, my phone starts getting hot. Then, the battery also starts draining so fast, it could go like 10% every 10 minutes. This never happened but just started 3-4 days ago. (Today is Sept. 1)
I'm not using location services, mobile data a.k.a. 3G, bluetooth, iCloud, etc.
I just need to know why this is happening and how it can't happen again.

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Is it best to get it from BestBuy or Target or Walmart or Apple store?
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