I'm back with an update. Sorry for the long post, I'm trying to bring all the relevant details.
Tuesday the new motherboard arrived, it's an Asus Prime X570-P (at first I ordered the MSI MEG B550 Tomahawk but it would arrive early December so I canceled that and went for something that was in stock). Installed it, connected everything, equipped all four DIMMs, no POST. No beep, nothing. At least fans don't go stormy and long-pressing the power button is able to shutdown the machine. I tried many times, and a few attempts gave me some beeps. Sometimes long-short-short, other times just the first (long) one. But not the normal POST beep, which is lower in tone and more pleasant, as I later found. Nothing was displayed on screen during these attempts.
Started disconnecting things, and
it seemed not to like one of my front case fans, as it POST-ed with it disconnected, only to go back to no POST when I reconnected it. But this was just another chaotic and nonsense behaviour, as further tries resulted in POST with the fan connected as well as no-POST with it disconnected...
After maybe one hour of frustration, although haven't identified a cause for all this, I got it to consistently POST so I refined some BIOS settings, enabled the DOCP or whatever Asus calls the XMP, 3200MHz seemed to work just fine, closed the case and moved it on the floor, where it usually stays. Again, no POST. Put it back on the bench in horisontal position, all ok. Back on the floor, tower position, not ok.
Ok, damn you, back on the bench but in tower position. Wouldn't POST. After a number of power-offs (via power button long press) the following screen appeared:
Which seemed to suggest that it doesn't like the memory @3200...
I really should have written down all that happened, because I cannot remember if after this I let it at the default 2133 or brought it to 3200 one more time

, but anyway soon it was back to non-POST-ing. Again,
it seemed that disconnecting three things - SATA cable towards the BD-RW and the USB 2.0 and 3.0 cables that go to the front panel would solve the problem, because it would work after that. I used it like that for the rest of the evening without further problems (at this stage I'm sure the memory speed was 2133, although most certainly automatically set by the BIOS when it presented me the "POSTed in safe mode" screen, which I saw 2 or 3 times until then. Restarted Windows a lot just to check and it all went smoothly.
Wednesday I had a busy day, but still managed to be around the computer for some time. Starting, restarting, shutting down, everything ok. Moved it on the floor and it still worked

Got the RAM to 3200 and it passed a full memtest:
When I got back in the evening I used the computer a lot, benching, gaming, everything perfect.
Today I also used the PC a lot, then towards the evening moved the PC back to the bench and used my multimeter to thoroughly check the front USB 2.0/3.0 wiring/connectors and found nothing wrong. No shorts, no high-resistance paths between individual pins. So I connected them back to the motherboard. Can you guess what followed? No POST! Two times in a row I got the long-short-short beeps, then nothing. Restarted maybe 20 times and the "POSTed in safe mode" wouldn't appear any more. I noticed the fans on the video card behaving strangely:
Thought maybe it went bad somehow, but there was no beep even when I removed the video card!
I finally did get it to "POST in safe mode" after I started removing DIMMs and I was down to the last one... Quickly installed its pair, set them back to 3200 because that's the speed they're supposed to work, and here I am typing this at close to 4 a.m.
I'll make a last attempt to solve this by getting some new RAM, which will have to play nice with the 5900X on the TaiChi board. Yes, the Asus will go back to the store because of awful fan control and annoying active cooling on the chipset. Also, if the "simple upgrade" (yeah) I dreamed of turns out to be comprised of CPU+MoBo+RAM (instead of just the CPU), maybe it would've been better to jump directly to AM5 and maybe spare me this pain...
So please advice me what RAM kit to get (
[email protected] I think, but brand? and 2 or 4 modules?). Thanks!