Hey I used to have a really bad comp as well for quite some time and found quite a lot of interesting games out there that still worked on my pc without problems. A game that works is good, but it's also the question "how" it works. Some games are just unplayable even if they work somehow.
I can suggest you:
-Ragnarok Online(MMORPG with 2D character models and 3d surroundings it should work on your pc even if you can't use most 3D graphics)
-Wesnoth(Online turn-based strategy game)
-Phantasy Star Online Blue Burst(It's like a very very old Vindictus/C9/RaiderZ and is similar to the game Hunter)
-Minecraft(Sandbox game but not sure if it works, it's more consuming than it looks. Lots of private servers out there)
-Terraria(It's like a 2D Minecraft with more action)
My personal tip to you(if you like Pokemon but who doesn't) would be one of these fan-based Pokemon online MMOs:http://pokecyrus.net/
Warning beforehand, it's a very difficult game that uses a TP system instead of the EV system of the original.http://www.pokemon-world-online.net/
Really easy, like the opposite to the other pokemonMMO but not only for casual players I can assure you.
Also I can suggest you to play flash-based browsergames. They work on almost any pc and are not as boring as text-based browsergames can be.
-Tribal Wars(very addicting..only play if you got no value for your real life lol)
Hope I helped out somehow, not sure if you only meant MMORPGs.