Motherboard standoffs are important and you shouldn't skip them. A case from a good brand will always have all the motherboard standoff screws screwed in out of the box. However, if that's not your case of if you are using a MicroATX motherboard on an ATX case and it doesn't have all the necessary standoff screws then you should manually screw them in holes available on the case. Most cases will include and set of screws in which you can find the standoff screws.
If you aren't using all available screw holes in the motherboard then there are chances that the pins at the back of the motherboard will touch the metal areas of the case and short. Modern motherboards have protective features that will prevent it from booting if something is shorting out, so your PC will not boot.