The "maximum directx level" of your card is 7, so Half Life 2 is detecting that correctly. However, the latest Nvidia drivers are designed with the latest cards in mind. You might want to try some older revisions. Nvidia hosts a driver archive , so try something in the 4x.xx range (perhaps 45.32) or, if nothing there works out, something in the 5x.xx range. Maybe even look into 3x.xx.
On the other hand, you're missing out on all the new graphical "shinies" Half Life 2 supports - perhaps it's time to look at a new video card? ;)