Ok, the stock cooler push pins have a locking mechanism. Now, they are twist locks and aren't extremely hard to break the lock for the twist mechanism. What you need to do is pull it off of the CPU and check that they still will fall to the lock and twist and actually lock while off of the motherboard. If you broke one, there is a way to pup them out of the retainer and use a bolt-on method. HOWEVER, it requires a drill, 2" or longer machine bolts that will fit through the mobo HSF holes, felt washers, rubber grommets, and other non-typical household items LOL. I actually have an old E5200 with the stock cooler bolted on. I'll see if I can find that machine tomorrow after work. I believe it's in my attic of death storage area.
Eitherway, you need to double check those retention pins. Remember, the twist should unlock/lock it only when it's depressed. The rest of the time it should spin freely.
Now for my second question here. Does that unit have the copper or aluminum insert on the coolers bottom? If you knock that loose; that can be part of the problem and you'd have to TIM that and the CPU during installation. I haven't seen the 540's stock cooler but if it's solid without an insert like the Exxxx series was, then it's pretty much guaranteed to be the retention clips.
As for bending a fin, you didn't hurt that HSF. The one single advantage of the stock cooler, aluminum takes longer than copper to heat up. This means it actually can work better than copper until it actually heats up. So it takes more time to heat it up and if the fan is running correctly; a few bent/broke fins won't hurt it's performance all that much; especially how bad you're showing.
Take that cooler off and make sure you're setting the clips right. If I had a stocker left here I'd show you how they break and how to "remedy" it.