New iPhone 5 / Says No SIM, even with SIM! Paying for Help! :)

Question

I'm going to make this quick! :/
PLEASE READ THE WHOLE THING!
I just upgraded from an iPhone 4 to a iPhone 5.
I cut the SIM card with a SIM card cutter. Micro to Nano.
I use AT&T, and I'm just a teen.
My new iPhone 5 just arrived!
I bought it off eBay, from a trusted seller.
It is real, and when I booted it up for the first time, it sets it up, and asks to put in a SIM card to activate it.
I put it in, and it acts like I didn't even do anything.
No "Searching..." or anything!
It just stays at "No SIM", like when it arrived.
Here is the phone I bought:
goo.gl/QClXyj
It says, "With Contact."
All I know is, is that my family uses AT&T and pays every month or whatever.
We have data plans, 10GB Family Shared.
I asked the seller if it would work, right after putting in my SIM.
I also asked this other person from other forums, and he said yes.
I took it out, blew on it, no dust or anything.
By the way, I put the SIM card back into my old iPhone 4, with a nano-to-micro adapter and it works, so the SIM card isn't the problem. (I think.)
I tried rebooting the phone, etc.
Please help, thanks!
<Edited by Host>

Answer 1

I FORGOT TO ADD!
IT DIDN'T COME WITH A LIGHTNING CHARGER!
I WILL HAVE TO BUY ONE ONLINE SOON.