Those pins are annoying indeed, but i don't see how reseating the whole thing would help... Thermal paste replacement, is it easy? And would you recommend me just doing it?
EDIT if I know what pin's you are talking about, haha. I think of the ones connecting the fan the the metal doobelidoo
I'd only do that as a last resort, especially for a first timer and especially with push pins. But unless there are some other ideas, we might be there.
The push pins connect the mounting bracket for the heatsink to the motherboard. Each is a little plastic spike with rod in the center. The spike is actually 2 pieces. When you push down on the pins, that pushes out the rod and that splays (pushes out) the tips of the spike to lock it into the board.
The problem with remounting those things is
1. it's impossible to get the tips close enough together again so that you can get them all to back into the same holes at the same time. You have get 4 binder clips and some super glue (cyanoacrylate), glue the tips together (make sure rods are retracted) and hold them with the binder clips for an hour or so. Then you can wiggle them in. The shearing force of the rods being pushed down will break the bond of the glue.
2. You have to use a fair amount of force to push them down enough to lock. As long as the motherboard is properly mounted, that's not a problem, but it's going to feel wrong - like you're using too much force. If it's not properly mounted in the sense that there isn't a standoff (metal screw that 'stands off' from the case) under every mounting hole, it's possible to crack the board.
If that's you're only option, I would seriously consider calling the builder and asking him to help you out.