I am aware now that Mathematica 10.0 is having difficulty with freezing during its startup while displaying the message "Initializing kernels..."
The question is answered here:
Mathematica 10.0.x freezes in Initializing kernels
Unfortunately, I'm just a grad student in my university's math department, and I have very little knowledge about programming in general. Can somebody please explain to me the steps that I would have to take to start a standalone kernel, and what exactly a paclet is, and how to evaluate it?