I have a Intel Core Duo CPU E7400@2.80GHZ and my GPU is, I guess, a ATI Radeon HD 3450. I think, im not sure how to check for sure. It says that under Device manager and Display adapters. Also, I have 2 gbs of RAM. i know my GPU aint great. Really, the only games Ir eally wanna run on this thing is Warcraft looking and running good, The occasional Steam Sale games I might wanna get, and Old Republic and Star Craft 2 when they hit, and Also Oblvion and ahve it look better then it does on consoles.

yes. will run just fine. your computer isn't terrible but you need to make sure you don't spend more than 150 on a new card because your memory and cpu are gonna bottleneck you at a certain point. you should be able to run most games on high at 1024 resolution with that setup and a 150 dollar card. look at the radeon 5770 or 5750.
 
Also, don't see why you couldn't run those games right now on the machine you mentioned. would run just fine on medium or low settings on 1024.

just spent 1150 dollars on a new pc. just the tower, not including the monitor and keyboard/mice/speakers. It is pretty much top of the line everything. you can get away with 800-1000 if you use your old hard drive and dvd drive. otherwise expect 1000-1250 for a really awesome system. A mid level system could be done for 750
 
 as far as bioshock clogging up your card. doesn't suprise me but sc2 and old republic do not take much gfx at all. the guys who made old republic said it will be on par with world of warcraft.  

I'll link my system here in a minute with prices for reference.
 
 

Also, keep in mind how much wattage your power supply can handle, don't want to go installing a 5970 on a 400 watt power supply and watch your computer blow up.

even with 2gb ram you will notice a huge difference in performance with a new gpu.. and im pretty sure what you have will handle sc2 ;)

the 9800gtx is now known as a gts 250... and no the radeon 5770 is not far behind a 4890 and is comparable to the gtx 260 not the 9800 gtx... at the moment a 5770 is the best bang for your buck if youre on a budget at ~ $150-160

upgrade the ram to 4gb, if your using vista it makes a big difference.

You might want to think about you're own build if you really want to get into it. But for now, a little extra ram, a cheapish gpu, and a decent power supply for the gpu will get you rolling nicely.
 
@drakattack: You should list what you got there. New computer parts are the best.

" @drakattack: Well, I tried DLing teh Bioshck 1 demo on Steam, and that thing barely loaded and chugged to hell and looked like ass. I think Star Craft 2 adn Old Republic are going to require jsut as much if not more then that game. "

Nvidia GTX 460 1gb. Unless you are looking for a hundred dollar or a five hundred dollar video card this is the only option at the moment. I am running pretty much the same processor, two gig of ram, even with an 8800gt I could max out Oblivion, SC 2 and WOW and not see my performance dip below 60fps. The GTX460 is well over twice as powerful as an 8800gt

I give up trying to post links to my gaming system. GB is failing miserably atm. 
 
Gigabyte GA-X58A-UD3R w/ sata 3.0 usb 3.0
Intel i7 930
palit gtx460 overclocked sonic edition
6gb gskill 1600 tri channel memory
850 watt power supply with blue led 
thermaltake armor a90 case with blue led   
1TB 7200 rpm
80GB SSD
 
Got it all for 1129 with shipping included. Had to use some bundling sku's and a promo code to achieve the price. Will be using my old G15 gaming keyboard and mouse. Sound will come via the onboard 5.1 controller and I am using a 5.1 logitech speaker system I had laying around. I will be playing on a 23" lcd.

i just recently finished building my PC at medium/good budget.. 
Intel Core i5, 4GB DDr3 RAM, 1TB HDD & ATI Radeon HD5870... imo this is a decent PC which should let me run all current + upcoming titles... probably will upgrade the ram to 6-8GB next month :)

A videocard is purely the thing that renders videogames. Your you have to becareful a cpu doesn't bottleneck a videocard by it's speed, however 2.8Ghz is no problem at all however your cpu isn't great either. It doesn't hurt to add mor ram, might help with loading stuff faster. Still your right, the videocard is completely responsible for running graphics, so that's what you want to upgrade.

 
I hope you have enough power to run the videocard from your power watt supply. Everyone is recommending the GTX460 right now, it seems to be great value right now with enough power. It's better to get the 1gb version, however it should definetly improve your gameplay experience.

OP: Your current computer is a good start.  As others have said, the video card should be the first to be upgraded - I can't believe you tried to run BioShock on that POS.  A 5770 is a great cheap card - in can play everything out today and look good, and it's ~$150.  It doesn't require a lot of power either, but you should check your PSU to make sure it can handle something beefier than your 3450.  If you have some money after that, I would double your RAM - you probably have DDR2, so it shouldn't be too expensive, <$50.  
 
My system CPU is similar to yours - Pentium DC E5200 OC'd to 2.93GHz, 4 GB RAM, HD 4830 - and I haven't found a game that it can't play.  I can't max most games, but it always looks good.  I built it for ~$550 a little over a year ago, without monitor or input devices.  It won't last as long as drakattack's new rig (which will kick some serious ass), but it'll last a couple years.   My point is, if you spend $200 on your current system (depending on your power supply), it'll last you a couple years easy, especially if it's focused on running The Old Republic and StarCraft II - mass-market games like those won't require beefy systems. 

Just bump up the graphics to some cheapo 8800GT or some 2xx series and you'll be fine with that GPU CPU combination for the next year or more. There aren't many PC exclusives left and you can certainly play ports with that config. 2GB or RAM is enough if you background process list isn't a mess.