This sounds just like the issues i used to have when Blender needed more RAM than i had. Or when it needed more VRAM(thats whats used when rendering on GPU)
I solved my issues automatically when i got a new PC, but you should make sure your computer meets the requirements for your scene, if it says at the top that the scene uses 2 gigs of RAM then make sure you have twice that when rendering.
For example, a subdivide modifier on any model increases the number of vertices by a lot. A plane made up of 4 vertices then subdivided will get you 9 vertices if im not mistaken, then it keeps going up more and more for each subdivision you have on the model.
For more complex models this will increase even more and it is VERY resource demanding, that coupled with complex materials will demand every ounce of power your computer can muster. Sometimes a standard desktop is not good enough to render a complete scene filled with complex elements, thats why you should try to render it in layers and stitch it together in the compositor.
Am i waay off or close to your problem with this lengthy text?