I'm sorry, but your estimation of $1600 minimum for a gaming PC is ridiculous. Even if you can't build a higher-spec PC for the same price as a console ($~600), You can get close, and the performance will still be better and give you all the good things that PC gaming brings (e.g. discounted prices EVEN BEFORE RELEASE, controller compatibility, VR support). And if you're willing to go with a Top-Tier last-gen GPU, you'll get AMAZING value for your money.
As far as the test PC having issues, I agree with what others have said. If there was an OC applied and all of a sudden the PC wouldn't boot, the first troubleshooting step is definitely to turn that OC off and make sure it boots with stock settings. That being said, overclocking is NOT necessary for most modern games, so you're just wasting time worrying about that if you aren't a power user.
As for parts availability, yes it's a travesty of supply dearth as far as general availability is concerned. However, there are ways to drastically improve your chances of getting one of these new cards. I got an ASUS Strix 3090 for MSRP from Amazon because I subscribed to an Anti-Scalper discord server that implemented a web-crawler to provide stock notifications. I happened to be on my phone when the notification came through, and hit Buy It Now on Amazon 5 seconds later. It's not impossible, it just takes dedication. If you really have your heart set on it, it's entirely doable.
And finally, Laptops aren't enough. The price/performance for laptops just isn't there. You would really only go for a laptop if you're willing to compromise on performance (assuming Price is an object).
You also never mentioned pre-built systems. Maingear (for example) makes some very affordable pre-built desktop systems that give you some pretty amazing price/performance, not to mention that as a system builder, they get access to the new GPUs when others (read: consumers) can't. Totally viable option.