I downloaded the game, installed it and all that, then when I started the game it stated that my computer didn't meet the requirements (although it most definitely did and when I checked the config file it said that all the settings were on medium or high) and when the menu showed up, the logos flashed by really fast, the framerate was way too high for the first few seconds, and then the menu buttons weren't displaying.
Edit: I just started playing, and in-game, the game is fine except for one thing, every couple of seconds, the framerate jumps to a really high level for a moment or two. I still have the disappearing menu buttons problem.

Try disabling sound acceleration from your directx config utility (run dxdiag -> sound -> sound acceleration slider, reduce or turn off entirely).
If it doesn't work, post your machine, OS, and graphics card / chipset. Oh, and also try to run as administrator if you're on Vista.

The disapearing menu buttons bug is still present, but slightly less frequent. The frame rate jump problem is still present.
System Model: HP Pavilion dv6000
OS: Windows XP Professional
Graphics Card: NVIDIA GeForce Go 7400

Nope. It's not a multicore system.

You could always try setting the Compatibility mode back. You never know.
And of course, make sure your drivers are up to date.
Also, try going to your start menu and try running Postal 2 in Safe mode.

I posted a support ticket for the same problem. I'm googling it also I'll post back if I find anything.

i had the same problem but a multicore system, solved it by tweaking the affinity

Note, compatibility mode seemed to fix most of my problems. Just immediately had a crash as I was messing with settings however. Thanks for the solution.

I must say, this is sorta embarrasing, today, when figuring out a solution for a problem with Serious Sam, I discovered that this laptop actually is multicore, so the affinity solution could probably be the solution. Resintalling the game now, will post my results when I get a chance.
Edit: The framerate is fine now that I've changed the affinity, but the menu buttons still aren't displaying all the time.
Edit 2: Now the whole game is running in slow motion, I don't mean that it has a low framerate, I mean that everything is, yeah, in slow motion.
Edit 3: My problems are mostly fixed. I still get occasional problems but overall Postal 2 is working fine.