New to PC gaming -- help?

Hey, so I haven't really bought a PC game in like 6+ years and don't really know what is on the market or what to buy. My PC is brand new and has some pretty nice specs and should be able to handle pretty much anything.

The last games I really remember enjoying were SimCity 4 and the RollerCoaster Tycoon games. I enjoy as much of a challenge in a game as possible.

Also, I'm not crazy about shooters, but am otherwise open to just about anything including action, fighting, or war games that isn't a direct shooter.

My only other requirement is that it is not an only online crap with DRM or some EA rip-off style game (not to get into that discussion). Preferably I'd like to avoid EA altogether, but I'm open to changing my mind about that.

Any suggestions?

What about XCOM: Enemy Within, Battlefield 4 (yes an EA title), CoD: Ghosts and Assassin's Creed 4. Also Terraria, Minecraft and Starbound are pretty good if you like exploration and resource games. Keep in mind that Starbound and Terraria are 2D-sidescrollers.

Check out Steam if you haven't already.

People are still making Simcity 4 buildings at www.simtropolis.com

There are lots of strategy games like Civilization, Sins of a Solar Empire, Europa Universalis, Tropico, and more!

Get Civ V.

Get a Steam account! While it is a DRM service, it is not always online and there are plenty of great seasonal sales!

Out of curiosity what are your specs?

Seriously, get steam if you haven't already. You just missed out on some killer sales. The PC market is huuuuuugeeeeeee, just take a look around and pick up whatever takes your fancy. Although i would say if you're picking up a game for online only primarily, check to see if servers are still running, and if there's at least some community still hanging around (which is usually the case with PC games). Also MODS! :D

Download steam.

Christmas sale will start in a week or so and then you can fill up on games :D