External Hard drive not recognized/erased

Ok,
So I recently got fed up with my old Compaq laptops and got myself a mac all in one.

I was told at the Apple store that I can use my external hard drive on both the mac and the compaq. I tried to use it to put my files on the mac, but when I did only some of the files transferred, and when I went to open it up again on the compaq, it would not detect the external hard drive at all.

So now I do not have 90% of the files, and no computers will detect the external hard drive.

I bought a file recovery program from seagate, but that's confusing as well.

I want to be able to get my files back, and use my external hard drive again. I'm not sure if either is possible...
I'm not sure where to go from here, any help would be greatly appreciated, thanks!!!!!