Hi nice of you to upgrade your sons rig! I can see you've been looking into it but you seem to have a couple of wires crossed. I'm sorry I'm going to really rain on your parade but this is kind of how it is at the moment.
System RAM is DDR4 and is not obsolete, graphics cards have GDDR5/6 RAM etc, these are totally unrelated and compatibility between them is not an issue.
The CPU and RAM are a very good choice.
Motherboards off the shelf come in standard sizes with the same hole placements for compatibility with DIY cases etc. OEM machine makers sometimes use bespoke parts that are only compatible with the cases they use. I found a forum post which suggests that the case you have uses a standard Micro ATX (M-ATX) sized motherboard. You need to really double check and make sure that's actually the case, if its a proprietary size then you cannot change out the motherboard.
The board you listed above is a good one, but unfortunately ATX sized which is larger and so wont fit in your case even if it is M-ATX compatible.
Another problem is the state of the graphics card market, its almost impossible to find cards for sensible prices at the moment so I cant recommend anything right now. It's set to last until at least next year if predictions on chip supply from experts turn out to be true.
The 500 W power supply you have in that machine will also not be enough to reliably run any of the 3000 series Nvidia cards, or any of the current AMD 6000 series graphics cards, even if you could find one for MSRP. Also the physical size of your system will limit the card that you can fit inside, even if you could replace the power supply. Higher end cards have large heatsinks and coolers that don't really suit small cases well, if at all.
Finally, the copy of Windows 10 that come with your machine will be an OEM copy. That means when you change out the motherboard your license will no longer be valid, and legally you would have to buy a new one.
A) Find a second hand 7700K to install. I wouldn't pay more than 200 USD absolute tops. Add in a second stick of cheap 8GB DDR4 RAM, with the motherboard you have it will not run faster than 2133 at standard settings so anything will be fine, and should run without issue. The 7700K will be noticeably smother then the 7400K in many games, and the extra RAM will also help a lot. I would also suggest an SSD, see below.
B) Keep researching parts, save up the money for a year until graphics cards are more reasonably priced again, and build a system from scratch that will not have any of the above problems. At that point you should be able to put together something for $1000 that will provide a much better experience overall.
C) If you are set on the Ryzen 3700, new motherboard, RAM and new copy of Windows, and it will fit in your case
. Something like this would be a good start, and carry over to a new build later on. The SSD is a must in 2021, the difference it makes to using the machine overall is not worth missing out on. I would go for a 1 TB model but I'm not sure on your budget and 500GB is enough for Windows and a game or so depending on the install sizes.
PCPartPicker Part List
CPU: AMD Ryzen 7 3700X 3.6 GHz 8-Core Processor
($319.99 @ Newegg)
Motherboard: MSI MAG B550M BAZOOKA Micro ATX AM4 Motherboard
($119.99 @ Amazon)
Memory: G.Skill Ripjaws V 16 GB (2 x 8 GB) DDR4-3600 CL16 Memory
($99.99 @ Newegg)
Storage: PNY XLR8 CS3030 500 GB M.2-2280 NVME Solid State Drive
($62.99 @ Amazon)
Operating System: Microsoft Windows 10 Home OEM 64-bit
($108.78 @ Other World Computing)
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2021-04-05 14:17 EDT-0400