BC was originally written for WinXP. I have it installed on 2 of my systems: one with XP and the other with Win7. Both are running perfect but I'm getting much better frame rates on my Win7 machine as the specs are even more powerful than your new system. However, I did get some "issues" similar to yours when I first installed BC on the Win7 PC. I changed the graphic drivers and it fixed it completely. You might need to try doing that... just make sure you properly and
completely uninstall the current graphic drivers before installing the new ones.
Also, it might help if you right click on the BC icon and select "Compatibility Mode", I think Win8 still has that feature - but don't quote me on that, then within the window, select the OS that you want BC to run in. This technique doesn't always work though but it's worth a try.
BC is a 32bit program and your OS is 64bit. Therefore, whether your running BC in native Win8 or in some compatibility mode - it's still running in emulation mode because 32bit apps have to run in a software emulator within a 64bit OS. That unfortunately,
sometimes introduces "problems" of a myriad of unknown types. Win7 has a much better emulator than Win8 so BC runs great on it - especially on a fast system. But, good ol' Microsoft in there "infinite wisdom" decided to modify the emulator in Win8 and "improve" upon it. I have heard in
many different situations that it in fact is crap compared with Win7's. Let me just say that you couldn't pay me enough to EVER get Win8... and I'll just leave it at that.
As far as changing the resolutions of game play, you could open up the options.cfg file and change the different res that you would like to the game options menu. But this also doesn't always work. Make sure you make a backup copy of the options.cfg file before you tweak the original. It worked for me but I've heard of others that it didn't. BC is a fickle program that is pretty individual at times from system to system.
Good luck and I hope some of this helps