I tried starting the game directly (not through launcher) and I got error reading: "Can't find entry of GetLogicalProcessorInformation procedure in library KERNEL32.dll" (that's loose translation, so maybe message is a bit different in english Windows).

I can't start it too, but I don't see any error.
When I double-click on any executable, nothing happens :\
(I'm on Xp with only 1.5 Gb RAM and a single-core cpu, however..)

EDIT: nor a black screen, nor anything in Eventviewer.

Same here. When I start the game (no matter if from Galaxy Client or directly, no matter what compatibility settings are active) I get a black screen and then I am back at the desktop. Game is displayed as still running, when I click on its icon in the taskpanel the same thing happens again.
Windows7 x64.
Message in Eventviewer:

[i]Fehlerbucket , Typ 0
Ereignisname: PCA2
Antwort: Nicht verfügbar
CAB-Datei-ID: 0

Problemsignatur:
P1: AvP_Classic.exe
P2: 0.0.0.0
P3: AvP_Classic.exe
P4: unknown
P5: unknown
P6: 200
P7: -1
P8:
P9:
P10:[/i]

I tried reinstalling the game, but it did not help.
I also tried updating DirectX, but installer says that it's allready up to date.

I can't start it too, but I don't see any error.
When I double-click on the PLAY button of the GOG Launcher, nothing happens :\
Windows7 x86.

Does the game itself (not the launcher) work on Windows XP service pack 2?

I have the same problem as Despistaku. Nothing happens when I click play in the GOG launch. I waited 45 minutes to see if anything ever popped up, but it did not (the actual game process never started running and the galaxy process was taking up zero CPU in Task Manager).

Windows7 64
4 Gb RAM
ATI Mobility Radeon HD 4330

I downloaded newer version of installer (namely version 2.0.0.25), reinstalled the game with it, and now it works!

Chiming in to say I too can't start the game, at least from the launcher. I start the launcher, press play and...nothing. It just stays on the launcher with the play button slightly faded as can be seen in the attached screenshot.

I just downloaded the game today so it is the latest version (2.0.0.25)

Though I just tried going to the games directory and launched "AvP_Classic.exe" and that appears to work just fine. I haven't tried multiplayer however.

It's the one in your library.