You're right, you should just be able to put the .dlls in the same directory as the executable and it'll work. It's possible that sb6 is reliant on other .dlls that you have but your friend doesn't. Or more likely, your friend's .dlls are out of date. That is one route of investigation. It is interesting that the window opens up successfully, and then closes. To me, that points to a problem setting up your OpenGL context. Can you post the code that you call to set up OpenGL?
Another, and in my opinion, better route to take would be to remove sb6 from your application entirely and switch to another, more portable application framework. Sb6 is only intended for practice, if you want a more robust framework I would switch. Since you've only done a small project using sb6, now is also an excellent time to change over because the code changes would be minimal and (relatively :)) painless. Here are a few libraries I suggest:
SDL - My personal favorite. It'll do everything from setting up a window, handling input, networking, playing sounds, and even threading. And it (claims) to be completely portable. Be warned, however. They just went through a major update (1.2 to 2.0) and the documentation hasn't completely caught up yet.
GLFW - If you're making a dedicated OpenGL application, this might be a better option. Since it's built from the ground up to work with OpenGL (unlike SDL, which first and foremost is a windowing framework and doesn't care what you put in the windows) it's faster to set up to work with OpenGL.
SFML - Appears to be a varient of SDL. To be honest, I haven't used this one before, but if you like it, tell me how it is!
There are others out there as well, but these are the big three I've heard of. Let me know if you have any questions about running them.