I'm trying to move a bone on Blender. I can't do anything with it at all. I've searched through the menus and noticed the Location transform is grayed out.
This is because the bone is connected to its parent, which is normal.
Now you can give the bone an absolute location.
EDIT: If you expect to move a bone and have the connected parent bones follow, you could use IK (Inverse Kinematics). You can easily add this as a modifier on the bone.