SSD upgrade in old Mac, not being recognized

Ok so here's the gist.

I have an old Late 2008 Macbook that the hard drive crashed on and I replaced with a new computer a few years back. Now my kid is old enough to have a laptop and I thought it would be easy to just replace the hard drive.

I bought a PNY 120GB SATA-III SSD model: CS1311

I used a SATA adapter to plug into my newer mac to format the hard drive

I created a bootable OS X Sierra on USB

The only problem I am having is that the 2008 Mac does not recognize this new hard drive. The USB will show up when running Disc Utility from the startup menu, but not the new hard drive.

I have searched forever on forums looking for help but have found nothing that works.