So unless I've somehow blown the new Mobo, or it's faulty, it's looking like the cpu or PSU. Is there any way that I can verify it is the one or the other without replacing parts?
One way would be
get a PC speaker and connect to the speaker terminals. It should give you a 'beep' notification to tell you how far it gets in POST. The beeps are encoded, just look them up and it would give some clues.
Otherwise, you'll need at least a DMM: put it on a +12V lead and watch what voltage does as the system boot loops. If the voltage varies to an extreme, especially dropping below ~11.4V or above 12.6V, you'll know it's not regulating very well and that's a clue it's bad. A really good DMM can also measure ripple. That's not a good test, but it's something you can do without more sophisticated test equipment.
And at this point, it's probably good to just revisit some basics. Since you're having so much difficulty getting things to work it's definitely suggested you be doing this in a bench-test arrangement, with nothing inside the case. I like to lay my motherboard on a cotton towel on table top, then connect everything up (PSU connections, HDD's, monitor, keyboard, etc.) with it laying there. You could even put a discrete GPU in and use that if you had one in your build.
Triple/quadruple check connections. ESPECIALLY that they are tight and secure. I've seen way too many systems where they did not fully engage memory into the DIMM's as they didn't like putting that much force to do it. MAKE SURE the DIMM is clicked in and the latch(es) are engaged in the notch(es). Also make sure the 8 pin ATXv connection is secure for CPU power as well as the 24 pin motherboard. They're hard to get in, but it's easier on a bench top set up to make sure they are fully engaged and no pins are pushing back out.
And check for pushed pins as it's sometimes pretty easy for a pin in those flimsy sockets on the PSU cables to not engage and actually back out. Check each and every one of the 24 pin connector pins, it's a lot easier to do that with it laid out in a bench top test. Although desireable to have all fully enganged there's less likely to be an issue with the 8 pin ATXv connector at the CPU because all it carries is 12V and ground on redundant pins there.