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The old Lucasarts remakes. Monkey Island, The Dig, etc. Adventures, especially the older ones, arent that demanding.
Or Syberia, Tunguska, etc

I am Bread, obviously.

I think no one mentioned Papers, Please yet... One of the best pixelgraph game ever imo =)

I forgot about Banished.)

My suggestions:
Risk of rain: roguelite platform shooter game really hard at first, really easy near the end. I spent hours on in with my i3 laptop. Unfortunately, multiplayer is quite impossible to setup (5 years ago it was a mess to setup but it could be done, then I heard they bugged it out and never looked back)
Gunpoint: Fucking gunpoint! One of a kind stealth platformer. Another game I played on my i3 laptop.
Axiom Verge: a very good Metroid clone (imo) made as a sideproject from a guy that works for AAA games that was really into Metroid. Played it recently on my desktop, but I don't think it will be too heavy.
Owlboy: a metroidvania game that was in development for 2000 years after its Kickstarter. Worth it imo. Again, played it on desktop but it should run smoothly.
Escape goat 1 & 2: Puzzle games involving a goat in various levels. Disclaimer: it starts easy and gets pretty hard. The bonus levels are quite impossible.
Shovel Knight: well, I hope you know about it yet. Megaman inspired platformer that came out of a kickstarter where they promised stuff and then they actually delivered. 3 campaigns atm, 1 more is going to come. The game is fantastic.
Stardew Valley: You know. Incredible farming game.
Steredenn: roguelike shootemup that I'm not good at all to finish, but that I enjoyed really really much.
The Behemoth games: Castle Crashers, Battleblock Theater, Pit People. Good games, low graphics.
Papers, please: I'm not gonna explain. Good stuff.
Gunmetal Arcadia Zero: nice Zelda2-like game.
Dead Cells: This will probably run. Really good Metroidvania roguelike.

Games I don't know enough about, but have heard great things: Wuppo, Undertale (I know, I know), Slimesan, Shantae Pirate's Curse, Party hard, Nongunz, Downwell, Chroma Squad, Broforce, Brigador, Bastion, Transistor, Pyre (these 3 look like the may run), 1001 spikes, Don't Starve + Together, Flinthook, Keroblaster, Shu, They bleed pixels,

Also, there's a lot of point and click games if you're into that genre. Way too many if you look around.

P.S.: if you have a controller you should really play Super Meatboy. Should run on anything, really fun platformer.

CAPSULE: http://store.steampowered.com/app/303940/CAPSULE/

It's like Alien: Isolation, only for a toaster.

Tradewinds Classics . This game is a gem .

As some already recommended: you probably can't go all wrong with some older games like
System Shock 2, Half-Life 1
Avadon, the Black fortress, Fallout 1, the old Oddworld Games
some old p&c adventures like King's Quest, Ben There, Dan That, Time Gentlemen, Please!
or perhaps some simple puzzle games like Energy Balance or Lyne
(most games above were given for free at some point and it seems you have some of them, perhaps they are worth a try) :)

Faster than Light,
Any PDS game,
Prison Architect,
Democracy 3