I suspect you have created permissions problems when you reinstalled from scratch.
Even if you used the very same username, a brand new unique Security ID (SID) would have been created by Windows when you installed it.
You'll need to Take Ownership and grant yourself Full Control permissions to all your files on your secondary drive, assuming you don't just want to completely reformat it.
Photoshop tries to use the root folder of the drive for scratch.
I expect it's something like this, but I checked permissions for the root and Authenticated users and Users both have full control.
I'm going to add permissions for my username and see what happens.
One thing to check is that that HDD (the older, non-SSD drive), is set up properly in your BIOS. That little step is often forgotten.
BTW - did you also setup that drive in Windows Disk Manager?
I'd check both locations, just to verify that all is, as it should be.
Good luck, and I also lean toward a Permissions/Security setting.
SOLVED: I did mess with the permissions, but I think what did it was following some advice I found elsewhere related to Illustrator registry issues. I made the settings change then I found Photoshop in the start menu and right-clicked>run as administrator. That seems to have done the trick.