graphics card
Here are the important specs for your computer:
eMachines T2825
CPU: AMD Athlon™ XP 2800+ Processor (2.083 GHz) with QuantiSpeed™ architecture
Operating System: Microsoft® Windows® XP Home Edition
Chipset: NVIDIA® nForce™2
Memory: 512 MB DDR (PC 2700)
Hard Drive: 120 GB HDD 2
Video: NVIDIA® GeForce4™ MX graphics (AGP 8X slot available)
Sound: nForce™ 6-channel Audio
It looks like you have integrated GeForce 4 graphics so I highly doubt you will be able to run the game with some decent graphics. You might still be able to play it though, with everything at the lowest settings, I personally havent tried Half-Life 2 with that card, but I have tried games like Neverwinter Nights and Rainbow Six 3: Raven Shield and the settings had to be at the lowest to run. I recommend you buy a good video card for your AGP slot. You can get some pretty nice ones for around 100-200 dollars that will run HL2.