Which games can I play on an Intel Celeron 1.1GHz (up to 2.4GHz), 4GB RAM, or Intel HD Graphics 500?

You can play quite a few games, especially if you are willing to go old school:

Pirates

Thief 1 and 2

Sin (not episodes)

Baldur’s gate 1 and 2

Fallout 1 and 2 (also tactics)

Elder scrolls 3: Morrowind and maybe even oblivion

Classic Re 1–3 (Require some tweaking)

The original monkey island games

FF vii - ix (not remastered)

Soldier of Fortune 1

Unreal

Blood 1 and 2

Anachronox (JRPG)

Civilization 2 and 3

Blake Stone (original)

Half life its expansions

Sims 1

Neverwinter nights and toee (non hd)

Heroes of might and magic 1–4

Betrayal at Krondor

Utima vii

Unreal and UT classic

Quake 3 (Probably)

Revenant

Soulbringer

Diablo1 and 2

Throne of Darkness

Disciples 1 and 2

The dune classic games

Arx Fatalis

Wizardry (upto 8)

Quake 2

Hexen and Heretic

Beyond Good and Evil

Master of Orion 1 and 2(4x strategy)

Alpha Centauri

Carmageddon

Undying

Settlers (upto 3)

Deux ex (original)

Empire earth

Jade Empire

Kingpin

MK (upto 4)/ Street fighter 2/King of fighters (upto 2005)

Leisure suite Larry (classics)

Postal 1 (free on GOG)

Jagged Alliance 1 plus 2

(Just a few games that I can think of at the top of my head : )) You ought to find many more on Gog, Dotemu, and myabandonware as well.