Time machine issues with new MacBook air

Yesterday I bought a brand new MacBook Air.

First.

I tríed to copy my old stuff from my Time machine. When it was about to end the hard drive stopped flashing its light and the progression stopped at "about 3 minutes". I left it for a few hours and it didn't work.

Second.

As the process stopped half way I decided to format the computer and reinstall Yosemite. So I did. Everything seemed fine.

Third

I tried to copy my files again and process stopped again when copying settings. The disk stopped flashing light and I could eject it safely so I unplugged it and turn off computer.

Fourth

I turned it back on and had a forbidden sign on the screen when booting. I formatted it again and Now I'm reinstalling Yosemite.

The time machine disk seems to be completely fine and healthy. I ran a utility disk verification and it was all good.

My questions:

What am I doing wrong? I remembered this operation to be something rather simple?

Is a problem with my new computer or the disk, what do you reckon?

Shall I go back to Apple Store ?

All help appreciated.

I'm not a techie person. But I've got some common sense.

Gema