I have nvidia graphics. If I am using my external monitor with my laptop, twinview works well. But if I disconnect my external monitor, which is my primary display, I'm stuck. I can't get to a virtual terminal: I get a blank screen (since the virtual terminals are trying to display on the disconnected external screen). What should I do?

Your external monitor should not be your primary display if you have a laptop for this very reason. This is not a KDE issue, it is an nvidia issue. It shouldn't be an issue, though. Is dynamic twinview enabled? If not then you should add that to your xorg.conf. Did you try rebooting? If you can't get access to an external monitor, in the GRUB loading screen select your normal linux boot option, hit space, type "3", then hit enter. It should boot into a graphical display where you can edit your xorg.conf file. But KDE has no way of controlling nvidia cards, despite repeated promises to do so over the last several years Nvidia has so far not implemented the randr 1.2 support that would allow them to interact with the graphical screen configuration tools everyone else uses.