Okay, let me try and stop you before you waste money on a new PSU. The
only drives readily available to end-users where this 3.3V issue occurs are white-label WD Red drives "shucked" from external enclosures. Other than that, this is a datacentre feature that is never, ever implemented on consumer drives or PSUs. The addition to the SATA spec is
optional, and is not implemented in consumer-facing product for this exact reason - there's no support for it in any consumer-facing platform. If your drives worked on your previous PSU, they should work on your current PSU. You won't find a PSU supporting this unless you'd effectively need a server SATA backplane, not a new PSU. Each wire on a consumer PSU SATA power cable is linked to three pins in the connector, and these cannot be separated - meaning that getting a separate reading off
one of the 15 pins is impossible - that pin is directly linked to two neighboring pins.
On the other hand, if your drives are actually affected by this, the solution is simple: put a piece of tape (ideally Kapton, as it's a good electrical insulator and thermally stable) on the offending pin (but none of the others)
on the hard drive power connector (not the power cable!). Done.
It's as simple as that.
Now, I don't think this sounds likely. In fact, it sounds extremely unlikely, as
1) two of the drives worked in a previous PC, which is
extremely unlikely to have had a PSU with this functionality.
2) a brand new drive also refuses to work
3) they don't work in an external enclosure either, which isn't likely to deliver 3.3V through the SATA connector.
4) You haven't mentioned using shucked drives or refurbished datacentre drives off eBay.
My next question is thus: how have you stored and handled your drives since removing them from the previous PC? Not spinning up speaks to an electronic fault rather than a mechanical one - i.e. something like a defective drive controller or ESD'd PCB. I've never heard of an ESD'd hard drive (heck, ESD-ing anything at all is nigh on impossible these days), but it's a possibility. In theory there could also be some sort of error in the power delivery from the drive controller board to the drive motor, but I've never heard of that happening, and definitely not on three separate drives at once. Still: have they been stored together, or separately? Did they spend time disconnected from any system? If so, where, packaged how, and were they moved around? Did you ever have issues with the power supply in your previous build?
Lastly:
This isn't relevant, as it clearly pertains to SSDs (and possibly memory cards and similar flash-based products) and not HDDs. There's no NAND flash in a HDD (unless it's a hybrid drive), and no NAND controller. The 'No media' error simply means that nothing is detected as connected to your storage interface, and you got the results you got because memory card readers are (by far) the most common swappable external storage interfaces.