Sounds like the non-3D card laptop was running in a DX software rendering mode.
Blitz3D doesn't support software rendering mode. Bellieve it or not, your laoptop card does have 3D hardware, and DirectX compatible drivers.
DirectX has software rendering walkarounds for much of the basic Direct3D functions....which is what Blitz3D supports...Blitz3D tells Direct3D what to to and it does it (through the hardware driver)...But, if D3D can't do what it is asked (for a lack of hardware support, etc)...D3D calls on the software rendering side of DX to provide support...
all of this is spelled out in the DirectX SDK (Software Development Kits) that can be downloaded freely from Microsofts website for C/C++/VB etc..It's what developers like Valve to use for DX support in their games...