Screws are sometimes "locked" using a type of "glue" to keep them from coming loose, especially in settings where there is vibration (such as spinning disks). There are different levels of this locking material, some that are meant to be loosened and some that are intended to be permanent.
If this is what is holding your screws in, it is highly likely to be the removable type. Sooner or later someone needs to get into that case. You may need to use a bit more force than you think. But please heed BMitch's instructions about a tight fit. Generally you need to use the largest bit tip that will fit fully in the head slots.
To avoid stripping the head, you also need to apply downward pressure as you twist - to keep the tip from "camming", that is lifting out of the slot.