GameInformer

The lack of a discrete graphics card will be the limiting factor in games you can play.  Though the Intel HD technology has come a long way, it still can't handle most of the games you mention.   ...unless you are looking at StarCraft w\Broodwar (1998) or Fable: Lost Chapters.

Your best bet would be to look at games that released around 2009 or earlier.  The Warhammer 40k: Dawn of War series (not DoW II), Company of Heroes, or possibly even the original Torchlight.  I enjoyed StarWolves 3 but I'm a sucker for space games and strategy games so even the quirkiness of this Russian made title couldn't turn me off.

All offer solid, fun gameplay and you can pick them up with all their expansions for about half the price of a new game.  Impulse (GameStop) and Steam are your friend.

You can probably get away with playing any game from Valve with the exception of L4D. I know for a fact you can play Portal 2, so any games that use the Source Engine are probably games you can get away with. website to find out what games you can run: canyourunit.com

I highly recommend Psychonauts. It's an older game with an interesting plot line that gets really twisted towards the end, and I would argue that it's already fairly twisted in the beginning. Simple gameplay with good graphics except for the cutscenes, but who cares about graphics. You just missed the sale Steam had going a week ago, but you can grab it for $10, which is well worth it honestly. You seem to be more into fast-paced shooter/action games but I thought I would throw this game out there.

download Steam and try out the many demos to see what you can run.  Also head over to gog.com and pick up some older games for $3-$5 that will run.  Without a dedicated GPU your options will be somewhat limited.  

Braid

Give Plants versus Zombies a try! Also the Bejeweled series is pretty entertaining.

Getting Steam is a great suggestion.  They always have games 66-75% off as their daily deals and my first recommendation would be The Binding of Isaac.  Completely different from what's on your list, but I like what you like and this game is solid.

games.rofl.to/.../happy-wheels

yw

answers.yahoo.com/.../index - you can learn from this thread that i5-processors are second to i7 processors when it comes to gaming PCs. However, the lack of an integrated graphics card of your PC will decrease your gaming experience, but having i5 processor is a big catch for you

The i3 and i5 will do fine with most games today. The i3 is just a more enhanced version of the Core 2 Duo and I know of quite a few people who still have Core 2 Duo gaming rigs that can still handles todays titles; I had one myself until a month ago when I accidentally fried it. The thing is that laptops in general usually get their CPU's and GPU's slowed down so they don't overheat since all the hardware is in one tiny area. so a desktop i5 will perform better then a notebook i5 because the voltage is set higher meaning it can handle more tasks.

Also, for the notebooks in terms of GPU. You want a notebook with a dedicated GPU (Graphics Processing Unit) because it will handle games better then notebooks with intergrated (built-in) GPU's. An intergrated GPU will use the notebooks RAM to handle games; quite different from a dedicated GPU because it has its own RAM to handle games.

I would suggest getting a Silent Hill game, my laptop is way worse than yours but I can still play it.  You should get steam, they usually have amazing deals, especially around the holidays.

Try Steam. Im sure you'll be able to enjoy it

You can play some of the older games, but the more recent ones will be alot more demanding from your computer. If you haven't done so yet, try out Minecraft. There's tons of things you can do and it's constantly being updated.