I just successfully converted a 2007 model Mac Pro 2,1 to a 2008 model Mac Pro 3,1.
First, I'd like to clarify what Luigi60 wrote above about the PSU cable wiring. The ONLY difference in the PSU cable socket pinouts on the motherboards between the 2006 / 2007 model Mac Pro 1,1 / 2,1 and the 2008 model Mac Pro 3,1 is in the PS#2 / J2 connector (which is the 10-pin connector in the lower-left corner of the board, near the CPU-B socket). The difference is with pins 4 and 7 (the pin numbers are written on the wires side of the connector on the cable). Pins 4 and 7 are ground wires in the 2007 model Mac Pro 2,1, but in the 2008 model Mac Pro 3,1 pin 4 goes to the 12V1 line and pin 7 goes to the 12V2 line. Pin 4 needs to be connected to the 12V1 pin right beside it (Pin 5), and Pin 7 needs to be connected to the 12V2 line right beside it (Pin 6).
To fix it, I cut the wires coming from pin 4 and 7 (at the logic board end of the PSU cable) about 3 inches away from the connector, sleeved the tips 3" long pieces, then shaved the insulation off of the Pin 5 and Pin 6 wires right at the point where the sleeved Pin 4 and 7 wires would touch them, and then soldered the sleeved end of the Pin 4 wire to the shaved spot on the Pin 5 wire, and the sleeved end of the Pin 7 wire to the shaved spot on the Pin 6 wire. Then cover the other cut ends of the 2 ground wires (we don't need them for anything) and the soldered spots with electrical tape or heat shrink tubing (remember to put the heat shrink tubing piece on the wire before soldering it!)
You do NOT need to do anything to the PS#3 / J3 cable, or buy any new cables.
It's really a lot simpler to do than my description may make it sound. If you have the technical skill to rebuild a Mac Pro with a new motherboard, you can definitely do this cable modification easily.
Also, my Mac Pro 2,1's hard drive which had an installation of Mac OS X 10.11 El Capitan modified with the 32-bit EFI ("Pike" modification, I think it's called) didn't boot up after upgrading the computer's logic board to that of a Mac Pro 3,1. It would show the bootup Apple logo, have the progress bar go to about 2/3 of the way, and then the screen would go blank. For it to work, I had to download a fresh Mac OS X 10.11 El Capitan installer (from
https://www.macworld.co.uk/how-to/mac-software/download-old-os-x-3629363/ ), create a new install media (instructions below), then boot the rebuilt computer from installation disk, and reinstall Mac OS. When it asked what drive to install Mac OS on, I selected the same one that had the old installation on it (with the intention of overwriting the old non-working installation), but it instead did a repair of the existing installation so that when it was done the computer booted right into my old Mac OS installation, without having lost any data, settings or applications. Worked out great for me, but if you plan to do that I'd still recommend backing up all your data.
IMPORTANT: Make the new Mac OS installation media BEFORE disassembling and rebuilding your Mac Pro 1,1 or 2,1, if you don't have another Apple computer available!! You need a working Mac OS computer (probably x86-64 CPU-based) to make the new installation disk. I didn't realize this, and had to use another MacBook to do it.
To make the Mac OS installation disk, download the new Mac OS file from the above link, mount the DMG image, and run the InstallOSX.pkg file in it. Don't worry, it won't actually start reinstalling Mac OS. It only creates a new "application" on the computer, which if you run, it will start installing Mac OS. To create an installation media, don't run it, but instead use a terminal command that references it, which you can find here :
https://www.macworld.co.uk/how-to/mac-software/bootable-mac-installer-3575875/
Once you have Mac OS v10.11.6 El Capitan installed and running properly, you can try upgrading it further using the Mac OS Sierra / High Sierra / Mojave / Catalina Patcher tools.
If you are upgrading your computer's video graphics card at the same time as the logic board, and plan to upgrade Mac OS past the v10.11.6 that Apple officially supports on the Mac Pro 3,1, be sure not to get an AMD Radeon HD 5000 or 6000 series video card. The website says that those aren't compatible with the Mac OS Sierra / High Sierra / Mojave / Catalina Patcher tools.
The rest of the process is just as everyone else in this forum thread has written. Luckily for me the upgrade worked on the first try.
I am, though, having trouble with the fan speeds. The CPU_MEM and EXHAUST fans run at full speed unless I use a 3rd party fan speed control tool, creating a jet engine type noise whenever the computer is on. Also, the PSU fan isn't running at all. Does anyone here know a fix for that? I am using all the old fans from the Mac Pro 2,1.
I also am yet to do anything about the RAM memory card riser cage, which has a different mounting hole pattern on the new one and is a different size. So far I have just held the RAM risers in with their connector slots and packaging tape.
Here is how much this upgrade has cost me, in early April 2020 (all parts were sourced from eBay):
$46 for the new Mac Pro 3,1 logic board, model 820-2128-B / 630-7997
$22 for a pair of Intel Xeon E5472 CPUs
(Yes, the Xeon CPUs with a 1600MHz front-side-bus speed will work with 667MHz RAM sticks. No need to get new RAM)
$22 for a pair of new RAM riser cards, model 820-2178 / 630-8751. The Mac Pro 3,1's riser cards are quite different from those used by the Mac Pro 1,1 and 2,1.
$11 for a new northbridge chip heatsink
As for the GPU: I am yet to get one. I'll update this when I get one.
The NVidia GeForce 7300GT video card original to the Mac Pro 2,1 didn't work at all after the upgrade / rebuild (no video output at all). If you have that, you'll definitely need to upgrade it, but if you have something newer I'm not sure.
I've attached a pinout for the Mac Pro 2,1's PSU. The perspective of the image is looking into the plug of the connector on the cable. I've circled the 2 ground wires in cable #2 that need to be made into 12V lines to work with the Mac Pro 3,1's logic board.
Thanks to everyone on this forum who has provided instructions and experiences doing this. It really made my job a lot easier than it would have been without them.