Portal 2 lag problem

[the westfield has fallen]

I just got this game, and everything worked fine.

I started playing, and easily went through the scene in the relaxation room.

Everything went so good performance wise, until the first test chamber where I got a LOT of lag spikes and temporary FPS drops. At times I would get my usual, very smooth framerate but then it would drop down to something like 20 FPS. (I have all the settings on default BTW). This is getting really annoying and is peventing me from playing the game.

Here I have some of my hardware:

GPU: Gigabyte AMD Radeon R7 250 OC 2GB
CPU: Intel Core 2 Duo 3.00GHz E8400 Vpro
Motherboard: HP 3032h
Memory: 4GB

Please tell me if I need some better parts, or if there is a fix to this. I have a pretty good computer, It doesn't usually lag like this.