One thing I see is "VGA compatible controller: Intel Corp. 82852/855GM Integrated Graphics Device"
I'm pretty sure this is the problem.
Unless you have a deticated AGP or PCI-E Graphics card, you're going to fail 3D acceleration tests.
Do you have a graphics card in your AGP/PCI slot?
You could probably pick up a GeForce 5*00 for $30 or less on eBay. (My 5200 is good enough for ~60 FPS on Half Life 2 @ 1024x768)
Also, America's Army is native on linux (might have been a dream I had but I'm pretty sure it is) so it is most likely using OpenGL. Max Payne on the other hand is probably using DirectX. If you're running a DirectX game with Cedega, Cedega has to "translate" the DirectX in REAL TIME, so it's going to be slower. And if your graphics processor isn't a real graphics processor (ie, on board video) it's going to be a terrible experience.
PS, if you get a card, make sure to install then manufacturer's drivers for it (nvidia is better for this)! If you have any questions about that feel free to ask.
PPS, related to my PS,
my reply to your other thread