Part of your problem is you're using a MBR partition table, where Intel based Macs tend to prefer GUID. You won't be able to install OS X onto a MBR partition table drive, so don't get too attached to any data on the drive.
That said, I'd say this is a pretty classic case of a bad HDD bracket. Which is good, it's cheap and fairly easy to replace. The bad part is that you're unlikely to find this particular cable third party. So you might be able to convince some AASP in your area to sell you just the part, but it might take a little doing since they're going to make very little money off the sale.
And don't feel too bad. It took me 2-3X of running into issues like this before I stopped being fooled by it. It's easy to get taken in. I still regularly get units where someone initially diagnosed it as a bad logic board, and then I embarrass the crap out of them fixing it with like a $10 part. There are a couple of common issues that are almost always a bad HDD bracket, this is one of them. It also doesn't rule out that your old drive is bad either. It may well be failing, which may be why the new drive was detected and the stock drive wasn't.
I'v read about everything that was similar to my problem but I still couldn't solve it:
So here goes!
Suddenly my macbookpro (13") froze, I restarted it and got the blinking folder with a question mark (which is common for hard drives that does not function properly)
The next thing I did was trying to go into disc utility with my osx dvd, but I couldn't find my hard drive.
So I thought, ok it is my hard drive, lucky for me that I back-up every two days...

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