A lack of Power won't result in the System (Card) not Powering Up., especially given when not underload the Card will be drawing between 13 - 48w.
It's only underload will it peak at it's Maximum (Momentarily) before settling into it's Avg. Draw for the Application.
At this point what will happen during that Temporary Max Draw, is it will trigger the Power Surge Trip (i.e. More Power is being Requested than can be Supplied) … Advanced Power Control Interface will freak out and shutdown the System., almost identical to as if a Component trips the Temperature Sensor.. as it can even result in the need to switch off (or remove the Socket Plug) in order to reset the PSU to turn back on.
Keep in mind that the PSU can't tell what direction a Surge comes from (i.e. Socket, Motherboard or Device) it just knows one happened, so it's trying to be helpful and save your hardware.
Now as best as I can tell., there is obviously an issue with the Card itself (i.e. it has been damaged in transit)… the Fans not spinning up, well that can be caused quite literally by never reaching the Fan Stage of the BIOS POST; which could potentially mean that the GPU has become unseated (and requires re-balling) … an issue that wouldn't be possible if AMD would switch to Socketed instead of Embedded GPU Designs, this remains an absolute bewilderment to me given since the introduction of GCN these are "Complete" SoC, meaning for all-intended-purposes the Card itself is little more than providing VRM (Power), BIOS, VRAM and Display Links... all of which are basically identical.
As the (Solder) Ball Grid Array is the source of many board failures, especially as said connections can melt and warp over-time due to lack of airflow or such; well providing a Rigid Socket with Pins (either ZIP-PGA like Ryzen or LGA like Threadripper; doesn't matter) it in essence entirely resolves said seriously common issue.
Plus it would given how said GPU SoC are for the most part interchangeable, could allow AMD to sell them separately either as Replacements or Upgrades.
Like it made sense years ago for Graphics Cards to be Complete Solutions as they were comprised of Multiple Chips that were unique from Generation-to-Generation or even within the same Budget-Hyper Performance Processors (as they used to segment functionality and features)… but today it makes no sense for what., an extra $15 (Total) Production Cost?
But eh, w/e point here is... this is your likely culprit; which can either be done professionally quite easily (but is time consuming, as it takes about 45-80min in total not including creating the BGA Stencil; which can be a pain given these aren't typically provided "After Market", so they tend to need to be manually etched; this can take another hour or so. (Again another reason why Sockets would be better)
Yet, it could also be that a Micro-Transistor has been dislodged / fallen off / shorted out. In the past a common issue with Graphics Card Failures, well it was either DRAM (VRAM) developing a fault or one of the thousands of Micro-Transistors basically committed seppuku; and by the gods is that a pain in the rear to track down. As you essentially have to visually check over the board., if you can't find what's missing, run through the various Traces to discover the line that has a fault... it's just time consuming as all hell.
Had to do it recently to resurrect my Intel Pentium II that just randomly died., both the Processor Board (as they're on their own boards) as well as the LX440 Motherboard; which was a "Fun" Weekend... to be honest, if it wasn't a sentimental system., I'd have just thrown the parts in a box for "Salvage" in later projects and bought new from Electromyne.
What I'd suggest is RMA (Return to Manufacturer) and get them to refurbish / replace., honestly be the cheapest and easiest approach; and unless you Pre-Ordered and received it at Launch, well you should still be within Warranty; which typically only doesn't cover you if the damage was done via Overclocking … heck even then some will still actually be okay providing it, as well "Good Will" usually means next purchase will also be from them., so it pays forward for them to seem like they go above and beyond.
It's weird how some Companies don't understand this aspect of Customer Service, but eh... their loss.
