Note on Team Fortress 2 System Requirements Team Fortress 2 will require a directX 9 or better graphics card to take render the water effects, HDR lighting effects and other new graphics features. Many built in VGA chipsets will run the game poorly or may not even be supported.
Team Fortress 2 Minimum System Requirements CPU: 1.2 GHz Processor RAM: 256 MB Graphics Card: DirectX 7 capable graphics card Windows 2000/XP/ME/98 Mouse Keyboard Internet Connection CD or DVD rom drive
Team Fortress 2 Recommended System Requirements CPU: 2.4 GHz Processor RAM: 512 MB Graphics Card: DirectX 9 capable graphics card 256 MB Windows 2000/XP/ME/98 Mouse Keyboard Internet Connection CD or DVD rom drive
Team Fortress 2 Ideal System Requirements For running the game smooth in 1280x1024 with High Quality graphics.
CPU: 3.4 GHz Processor RAM: 1024 MB Graphics Card: Radeon X800 or Geforce 6800 Windows 2000/XP/ME/98 Mouse Keyboard Internet Connection CD or DVD rom drive
you would need to post your CPU and GPU information for anyone to say for sure, although I'd be banking on a no, judging by that the system ram is 504mb, as that would lead me to assume a onboard graphics solution which doesnt have enough memory.
Well there is dxdiag from the start icon, but the easiest way would be to download the free tool CPUZ, it will give a you a full rundown of the hardware available.