MarkoInBC

Figured I'd post what happened here in case there was any worth to anyone... I tried swapping the switch, nothing.  Tried a different Mac, nothing.  Moved that Mac to a different location (in case it was a wiring problem), nothing.  Turns out it's a problem with the Samba protocol.  Apple changed it after OS Mavericks (10.9) from Samba 2 to Samba 3.  Since that, there have been known issues apparently with Samba sharing of external drives over networks.  There were no really concrete options or solutions I could find online that would deal with that, so I downgraded the Mini to 10.9.5 and haven't had the issue since.

DO NOT BUY THAT AIO. I have used it and it is loud AF and I've heard stories of it failing a few months in. I'd get something like an H115i Pro or failing that an H100i V2

If you can connect the old drive to your computer, it will be as simple as drag and drop from one drive to the other for the pictures.  Games, you will almost certainly have to reinstall to work correctly.

I'm going to assume it's a SATA drive, and you should be able to connect it.  You should be able to remove it from your old system, take the SATA cable along with it.  Find a free SATA port on your NEW computer motherboard, and then connect the power to the drive.  When booting, you should make sure to boot from the new drive, not the old one you just connected.  If all goes well, you will boot into windows and you should see your old drive showing up as newly detected hardware.  Soon after, you'll be able to access it just like any other drive in your system.

I'm going to assume it's a SATA drive, and you should be able to connect it.  You should be able to remove it from your old system, take the SATA cable along with it.  Find a free SATA port on your NEW computer motherboard, and then connect the power to the drive.  When booting, you should make sure to boot from the new drive, not the old one you just connected.  If all goes well, you will boot into windows and you should see your old drive showing up as newly detected hardware.  Soon after, you'll be able to access it just like any other drive in your system.

If you can connect the old drive to your computer, it will be as simple as drag and drop from one drive to the other for the pictures.  Games, you will almost certainly have to reinstall to work correctly.