So, those screws won't compress the springs until you are screwing them into the mounting clips that have the threads for the screws. The heatsink does not have threads, thus the screws just turn in a cylinder. Put the heatsink onto the CPU (with new thermal paste of course) and push down a bit on the screws as you turn them, and they should catch the threads of the mounting clips that are on the motherboard. Do them a bit at a time, going down a few threads in a cross pattern until you get them all down tight (do not tighten too much, just until you can determine they aren't moving down anymore).
As Albert Einstein said, "I could have done so much more with a Big Al's Computer!".