For any future readers (May not be possible for everyone, but I was desperate and had the parts laying around, including soldering iron and the necessary skills):
When my laptop 2.5" SATA drive was failing I cloned it onto a 3.5" SATA drive I had spare.
I tried the SATA extension (See pictured lower) plugged into the 3.5" SATA drive and the laptop but it would not work.
I then proceeded to unplug the extension cable and cut the four power wires in half (two black, red and yellow wire) while leaving data intact.
After cut I wrapped the four wires from the laptop end in electrical tape (individually wrapped, then wrapped together), and soldered a Male Molex connector I had laying around (cut from something old before throwing away, probably cheap case fan) on the other 4 wires (making sure I got the pins correct (red to red, yellow to yellow and so on)).
After the SATA extension cable had a Molex connector fitted onto it I plugged the SATA extension cable into both the laptop and the 3.5" SATA drive.
I then plugged the Molex connector into a spare PC power supply (internal supply not in use), along with a PSU tester (See pictured) plugged into the main PSU ATX motherboard connector (Same can be achieved by joining ATX motherboard connector pin 16 and pin 15, More info on wikipedia See "Power On" pin in Wikipedia Table).
After that was all done I started the laptop and continued to use it as a temporary desktop (since setup wasn't portable).
After turning off the laptop I unplugged the PSU tester to turn off the PC power supply powering the 3.5" SATA drive.
Note: while this setup worked for me, I will not be responsible if you put the Molex plug on incorrectly and blow up the drive. So be careful and triple check your connections.
Also note My laptop still works and is still my primary computer, so it doesn't provide enough power through the SATA port even when the laptop is plugged in using it's power pack.
Quoted from Someone at whirlpool
You can't put a 3.5" SATA drive into a laptop because, even if it could physically fit in, the laptop probably doesn't deliver 12V to the appropriate pin in the SATA power connector, but there's no reason you can't use a 2.5" SATA drive in a desktop.