MagSafe won't charge MacBook

Okay so here is the story.

The MacBook is a MacBook7,1 (2010 Unibody) and I bought it second hand off eBay, but it was ex-office and it is excellent condition. I am actually amazed it looks brand-new. As well as it being in good condition, the seller also included a new MagSafe. The seller on eBay is a company that sells a lot of Macs and they have a very good reputation.

So I have been using it for the past 4 days and I love it, (it is my first Mac). On the second day, it was on my desk and I saw the charger LED changed to green and the laptop stated it was fully charged. So I unplugged it from the charger and went on my bed with it. When it got to 60% I plugged it back in again. But the MagSafe LED didn't come on. I tried unplugging and replugging at both ends, but still no LED, and the MacBook shows no signs of recognizing it had been plugged in.

What I have tried:

- Resetting the SMC (well at least I think I did, it requires the MagSafe to be in, so I don't know if it worked or not.

- Resetting the PRAM and NVRAM.

- Blowing any dust out of both the Mac's MagSafe port and the MagSafe end itself.

- Pressing the pins in slowly on the MagSafe and letting them spring back out again.

- Pressing the 'D' key to run diagnostics, but the Mac booted into Mavericks, so it didn't work.

- Holding the 'Shift' key to perform a safe boot, and it worked! When it was shutting down the MagSafe LED suddenly changed to green for about 3 seconds and then turning to orange. I thought great my problem is solved. So for some reason, I thought it would be a good idea to unplug the MagSafe and plug it back in to see if the problem really was fixed. Yep, it didn't work. Broken again.

So, I took the charger into a KRCS, which is an Apple reseller. They tested it on a MacBook Pro and it didn't work. So I was relieved my MacBook is okay.

My question is, why did the charger die so quickly, and did my MacBook cause it? Obviously I don't have a receipt for the MagSafe charger so I can't replace it. Also I asked KRCS to have a look at it to see if it is genuine or not. Because I really hate 'fake' or 'not-genuine' chargers. They said it looks real and they can't see anything wrong with it, it just doesn't work.

My questions:

- Could the MagSafe charger, even if it is fake, have harmed my MacBook?

- Could my MacBook have caused the charger to die? So buying another MagSafe would be stupid?

- Is a 60w charger enough for my MacBook, because I have heard the 60w charger can cause trouble with some MacBooks.

- And most importantly, why did it die so early?

The eBay seller has offered to send a new one out, I just need to send this one back. But there has got to be an explanation to why it stopped working so early.

Here is a video that describes the problem:

- https://www.dropbox.com/s/qc0wegqecphxg8i/Video%2022-03-2014%2020%2050%2001.mov

- Sorry if I sound moody in the video, I just really want this problem fixed, and if possible, without sending the charger back.

Some more information:

I only have about 15% left of battery, so I am saving it just incase any tips or suggestions require me turning on the MacBook.

Thank you,

Callum