Push Pin on Intel Broke

I've recently reseated everything in my computer but when putting my stock intel hetasink back in one of the white parts of the push pin broke off, the other side of its still on and it seems to snap back in. Was wondering if this will be ok...I noticed everything I was doing on my computer was getting slower like gaming and basic stuff...but at the time I didnt know about thermal paste, which since learning about that I've stopped using that computer until I get some more tomorrow. So is it possible that it's just the lack of thermal paste that's the problem or is because even though the heatsink seems to lock in it's not really?