Why doesn't this game work for mypc?

Does your PC have a dedicated video card?

I take it your pc has integrated graphics ? most games require a dedicated video card. IGP is poor at the best of times

Your PC's graphics fall short of minimum reqs.

Edit: Bear in mind HL2 was a couple years ago now!

Short answer: Because you touch yourself at night

Proper Answer: Integrated Intel graphics of ANY sort currently on the market is never going to run Fallout 3.

Buy a PCI-e card for £50+ , the cheap ones may not be great but at least you will be able to play the game.
Also you won't have to worry about not having a PCI-e power connector on that horrid Dell PSU.

i dont know how to tell if my card is dedicated

Video Card :



Motherboard without a dedicated Video Card :

A quick google shows that this is a laptop, so maybe the pics aren't so helpful OvrClkr  
BelialJ78 - Your pc isn't up to playing modern games, as it doesn't have a separate graphics card. The graphics are handled by a chip on the motherboard, that "borrows" memory from the main system. This is just to get pictures on the screen, and isn't recommended for anything but the most basic gaming. To be honest, I'm a little surprised it ran Half-Life 2. I was going to see if your motherboard was up to taking a PCI-E card, and suggest a few, but as it's a laptop, I'll have to steer clear.

Game needs an ATI Radeon X850 as a 'minimum' ?, seriously ?

You'd think they'd list ATI Radeon X800 XL, or GeForce 6800 GS / 7600 GS as 'minimums', since they're the lower/mid-range cards of that GPU series.

Most laptops are not good at gaming - even the ones 'built for gaming'. - Trust me.

You are absolutely right, I typed in the wrong model number by accident and it pulled up the Inspiron Desktop, anyways the OP's laptop has Intel Graphics Media Accelerator X4500HD, so it's a no show as far as Fallout goes. The board does not have a slot available for a dedicated video card, so there is no upgrade path as far as the GPU's goes.