PCIe5 Slot Black Screen-Reboot loop

Your situation indeed sounds unusual and I can tell you're quite frustrated. From what you've described, it seems like you've covered all bases: graphics card, motherboard, PSU, and different PCIe slots. The consistent issue is when you plug in your new RTX 4070 into the first PCIe slot.
Based on the error codes you're getting, it seems as though you're experiencing issues usually related to your GPUs or other connected hardware.
Error 116 can suggest graphic card instability while error 124 is often related to hardware causing system instability. However, since your computer works fine using the other graphics card or the RTX in another computer, we can't necessarily say that the graphics card is defective.
As for the WHEA Logger Event 16, it's often associated with incorrect voltage internally, specifically related to CPU voltage.
Here are a few possible causes or solutions:
1) PCIe Slot: Though you mentioned first PCIE slot it just doesn't work, you may check the state and setting in BIOS regarding the configuration for that slot. Some BIOS versions have hardware settings that need to be toggled to detect certain hardware. If the BIOS setting for PCIe slot is not properly configured, it could cause detection issues.
2) CPU issue: As you might guess, the issue may be related to the CPU as it contains PCIe lanes and it interacts directly with your GPU. Even a small malfunction can wreak havoc. You could consider contacting your CPU manufacturer or the vendor from whom you purchased the CPU and inquire about this.
3) Graphics Card Drivers: Since you mentioned that the problem occurs during the installation of Nvidia drivers, it might be a possible driver issue. Although the drivers work on another PC, they might not be compatible with the configuration you have on this one. Try doing a clean installation of the drivers. NVIDIA provides an option to perform a ‘clean install’ when you're installing the driver which will delete any old driver versions.
4) Power Issues: Although you've switched power supplies, power delivery could still be causing an issue. Even though it has fewer connectors, the RTX 4070 might be drawing too much power from the motherboard, causing instability and reboots. Check to make sure voltage levels are where they're supposed to be and the PSU cables are securely connected to your motherboard and graphics card.
Finally, if none of these solutions work, you may want to look into getting technical assistance or talk to the individual manufacturers about possible hardware conflicts.