To update, we got him a Westmere Pentium laptop for free, and not having a busted up screen / hinges seems to be enough to defer the question for a while. It is also a non-trivial upgrade over the C2D, however weak it is by our standards. It sounds like it's mostly good enough for Fallout NV at least.
I'm not angry, but I've been wondering how after I said this stuff I'm still getting >$500 recommendations from many directions:
is on a very tight budget, as in every twenty counts.
Sorry, I guess I thought it was obvious that $500 was already too much, and it probably wasn't. Worst case as a cap on cost would probably be the cheapest thing in some OEM's current lineup that still uses Intel's big cores and GT2, which should be $400 or less IIRC (probably less if it's a refurb or something, which it can be).
To update, it looks like i3-6100U machines are common enough at $250-300 on eBay, so let's say that's what we're trying to beat. Lower cost than that and/or more graphics power than that are the name of the game.
Worldwide median per-capita income is $3000/year. Even in the US, many struggle to put food on the table.1
We are incredibly lucky to be able to call "budget" something purely for entertainment purposes that costs $500-1000. That Westmere Pentium? It can game passably enough to be good entertainment. Forget anything 3D designed with the 8th gen consoles in mind, and forget most of the 7th gen blockbuster titles, but even if you restrict the field to just pre-2005 games and 2D/2.5D indie stuff, there are a bajillion great games out there that can provide endless hours of entertainment. That's
what I call budget gaming.1
I'll be happy to create a thread for this in R&P if need be (I debated doing so to start with, and cut some stuff out to make my thoughts fit here).