VirtualBox won't start any VMs (says kernel module is not loaded)

That’s yer prawblem right there, then. if, as you claim, you followed:

completely, then it would’ve looked similar to:

$ lsmod | grep vbox
vboxnetflt             32768  0
vboxnetadp             28672  0
vboxdrv               581632  2 vboxnetadp,vboxnetflt

So my next question is, how did you install it?