So you have a Dell laptop 1545, and it stopped booting into Windows Vista.
Then you were told to do a 'restore' back to factory settings, but it didn't work for you.
So you are now trying to take the hard drive out of the laptop and connect it to your other pc, a desktop? I think that is right.
It sounds as if your laptop's hard drive has failed in some way, so the 'restore' would not work anyway.
You need to prove if the laptop's hard drive is working. If you do any work to your pc's make sure you turn off the power, and pull the plug out of the wall.
The cable you bought will plug into the back of your laptop's hard drive, and the other end will plug into an empty SATA socket in your Desktop pc.
You will also need to plug a power plug in to the laptops hard drive. Look near the hard drive in your desktop for spare plugs.
If you are not sure about this, can you find someone who can do the testing for you?