For some reason when I play Ground Control on my laptop the game will not run above ~30fps - it doesn't matter if I switch from integrated to discrete graphics or turn all the graphics up or down or force vsync on or off, the fps won't change.
I played it a year or two ago on a desktop with a much worse graphics card and had no such issue.

I've tried every compatibility mode and various options on the nvidia control panel, all of which made little or no difference. I'd be grateful if anyone has any ideas on what might cause this rather odd issue.

Is there a way to completely disable the integrated graphics card (e.g. in the BIOS). I suspect the game to falsely using this chip and falling back to software rendering instead of hardware acceleration.

If you're using Windows 7 or newer, make sure your system isn't missing any DirectX9 components.
Just install this: http://www.microsoft.com/en-us/download/details.aspx?id=8109

That's indeed odd. While it can still be a Windows 8 compatibility issue, I've had another idea.
Maybe it's not the GPU but the (Multi-)CPU that causes the low frame rates. Ground Control might just not work properly on multi-core systems without further tweaking.

I found another guy in this forum who played with processor core affinity and according to him with some success.
Check this:
http://www.gog.com/forum/ground_control_series/command_lines_for_running_ground_control_and_dark_conspiracy_on_modern_systems

I tried setting GC to use just one core, but yet again no difference. It's perfectly playable at 30fps, just slightly annoying compared to having played it before with no such problem.

I had another go at this issue recently and managed to find a fix. The main problem as far as I can tell is related to Windows 8 dropping support for some older DirectX versions. For whatever reason it is possible to fix many of the games plagued by the resulting performance issues by running them in windowed mode (like MechCommander 1&2).

Ground Control has refused all of my attempts to force it into a window, but luckily I came across this DDRAW.dll. Simply copy it into the GC folder and the game should run just fine.