if you can check to verify, but from what im seeing, it looks like your graphics card is integrated and not a stand alone mobile gfx card. the problem with that is, is that the memory is shared between the graphics and the rest of the system. HL2 is also very Physics heavy... so its hitting the graphics card and its memory, plus the CPU and its memory... im a bit drunk watching the Bear game, and i dont have HL2 installed to check myself, but see if you can disable the Physics (maybe labled PhysX) in the game, and that may help alot.
also gotta remember that while yes HL2 is an older game.... it was completly revolutionary when it came out, and brought new systems to thier knees when it came out. and Valve never leaves good enough alone, they update the code quite a bit.
so im thinking that the integrated graphics with shared memory, along with the physics of the game may be your problem. course ive been drinking most of the day, so someone may come in and shred this theory.... but its what im thinking.
Man that sucks! I wish I had a REAL option other than "Buy a new PC" because I am not doing that to play a bunch of HL2 mods.