Their all the same. To be sold in the EU and America, they must all be certified the same way. No difference between one from Apple and one from a laptop charger. I had the problem when buying iPads with my dad for the family, we bought them in the US, but we needed European Adapters. We simply got a couple of the above mention cables and hooked them up - worked like a charm. Friend of mine lost his cable for his Mac Mini - I gave him one of the above mentioned and it worked.
The Hard Drive may have started to get hiccups (it what I call them), which may happen in a few rare cases, (I was one of them), just rescue all the data with the USB cable and put it onto a new Hard Drive.
Have you tried iTunes DFU mode to see if the Device is even still alive? Hold down the power and home button for 8 seconds, just to make sure the device is off. Insert the USB cable. Wait 60 seconds to make sure it has turned on. Hold down the power and home button again for 8 seconds. Let go of all buttons. Hold down the Power and Home button for 10 seconds. Let go of the Power Button and wait for 10 more seconds. Check to see if iTunes has detected the iPad.
Usually if you just install it to the point where it is done with setup AND personal setup, when the Desktop is first displayed, turn off the computer, take the Hard Drive out and move it to the other machine. My other recommendation if you have a FireWire Cable is to hook the Machines together and put the iBook you want to install OS X to into Target Disk mode by pressing the T key upon boot, hooking it up to the iBook 12, and running the installer on the 12-inch iBook, and ultimately just going through the normal install process, paying attention to install to the FireWire Target Media. If you mean that you just want to install it normally on the machine, I say go for it, it should work out fine.
Have you tried installing the latest SMC update for your MacBook? Mine had the same fault and after going to my local Apple Reseller and them temporarily inserting a new battery to download the SMC update I was back in business.