not sure if you want to just transplant your old drive in the new machine to run all your programs etc....this would not work since the hardware is different, graphics card etc.. or if you want to use a larger better hard drive you had installed in your old non working computer to the new one?.........(the a1226 should have a larger hard drive)
you can install your old computers drive, it isn't esp difficult to install but you will need a spuger to safely remove the hard drive ribbon cable that will have a glue kind of stuff and pop the tabs to lift the top case off..... a guide for hard drive install for both laptop models is here on ifixit showing the tools needed...... having some paper cups to put different screws in helps me keep organized.
You can export preferences from various programs and your files to the newer computer by mounting the a1150 old drive in a external enclosure. (external 2.5inch USB enclosures can be found on ebay for about $5.00).
and a small external is nice to have.