Hello everyone, my CPU died and I'm at a crossroads and hoping for some advice. I bought my rig 4 years ago second-hand. It was originally built in 2017 using high-end parts. It was not something I was looking for TBH, but at the time GPUs were hard to get and it was a crazy deal. Here is what's left of the rig:

• Motherboard - ASUS x99 Deluxe II, fits Intel i7 LGA2011-v3 CPU socket
• PSU - EVGA Supernova 850 T2
• RAM - 32GB, 4 sticks of G.Skill Trident Z 3200 DDR4
• GPU - EVGA 1080 Ti Founder's Edition 11 GB
• Case - In Win 904 plus - large and spacious case
• Storage - Couple of Samsung SSDs
• CPU Cooler - Have ditched the Corsair AIO, picked up a lowest tier fan for $10 to keep it booting while I figure out what to do

Options I'm floating.

1. Get a compatible CPU, but that socket is harder to come by for my MOBO and likely to be second hand + get a new CPU cooler, and upgrade GPU.
2. Replace MOBO, GPU, and get a new CPU and CPU cooler. The PSU is 6 years old but it's decent quality and 850 watts should be enough?

Price range/goals:

• Happy to spend a bit on something that is mid to slightly upper range, but not high end. Thinking $$ will go into the GPU and CPU (maybe $600-800 USD ea?), something reasonably good that's just before the latest gen to get a discounted price. If replacing MOBO, something simple and medium range would be ideal.
• Play some current AAA games like Baulder's Gate 3 and Elden Ring decently, at medium-high settings (not ultra), and don't need super high FPS.
• Ideally supports 4k resolution for desktop use but for gaming I'd be mostly sticking to 1440p/1080p.
• I don't want to overclock (those days are over)
• Likely to sell in 2ish years, don't need heaps of futureproofing
• If replacing MOBO, open to going to the AMD ecosystem for price/performance ratio. I've only ever used Intel so know less about AMD systems.
• Don't need raytracing, DDR5
• For CPU cooler I don't mind AIO but if anyone has any non-water cooled recommendations I'm all ears

I'm at a bit of a loss at what to do, and there are not many PC-building threads here on Tildes, so I thought I'd ask for some advice. Anyone have opinions on option 1 or 2 above, or is there a third option I'm not thinking of? And does anyone have part recommendations? Thanks in advance.

Here's the background...
So, I tend not to play video games at all any more (not for at least 15 or 20 years). My teen daughter wants to get a Playstation gaming console...but it seems less about playing and more about socializing with her friends. Her friends - while i promised my partner not to call them 'idiots' - are not really the best decision-makers and they're quite affluent (and we definitely are not affluent), so their poor choices usually never impact them. (I think it is less about being teens, and more about them being rich, entitled poor decision makers, because my daughter and a few other poorer friends are actually good kids who know that we can not get all the things.) Here's an example: all of my daughter's rich friends will ask their parents to buy them widget X, and so of course my daughter wants one so she can connect with these rich teens. For these rich kids, after they inevitably abandon widget X, there is no issue; they merely drop them off in one of the rooms in their mini-mansions. But for me, i can not always afford to buy widget X and then have my daughter abandon stuff in our little, meager but love-filled house. (Please if possible let's avoid the topic of how I'm raising my daughter, because all of the parents of us poorer kids in town have the exact same issues with our kids.) Now, we come to the part about my daughter wanting a playstation...I don't mind saving up for a PlayStation - especially if she'll use it...However, since she really only wants it to socialize with her rich friends via a couple of games, i was thinking on getting a PC/gaming rig (not as expensive as PS or some sort of AlienWare) instead of the dedicated gaming console, but still plenty usable for some games...So that, after some time if she abandons it (because for example her friends have migrated to other avenues of socializing), i can always re-purpose the machine. In my mind it seems a more worthwhile investment. (I'm a software guy mostly, but over the decades, almost every machine i have/own has been franken-built by me...so i know just enough hardware.) Now, if I go the route of a PC/gaming rig, can i just sign her up for online gaming accounts like PlayStation Network, and that will suffice for her to use her PC but still connect, say via PSNetwork, with her friends playing PS games?? (To help, i should clarify the games these teens play are fortnight, minecraft, and grand theft auto...I think GTA does not support in game chat/comms with friends, though i could be wrong.)

So, is it possible for me to sign up my daughter on an online gaming account - like PS Network - that would allow her to communicate with hr friends? And, if so, which gaming network should I set up an account, PS Network, Steam, etc.??? Thanks in advance for any suggestions!!!