I'm surprised if it didn't seat properly that it cooled the CPU at all and that the CPU didn't burn up.
Story time, lol.
My last build (AMD Athlon 1.2 Ghz) started out as a 1.1 Ghz machine. I bought all the stuff at a computer show. The HSF was re-boxed (as was much of the stuff there) and it had, amongst other scribblings, "Socket A" written on the box. Unfortunately, it must not have been for that socket.
After rushing home to get the build started, I immediately wondered why it was so hard to get the HSF on the chip. I had a "more experienced" builder friend with me and he said sometimes it was just hard to get them down. So, he took over and, eventually, managed to get it on. We got the whole build done and I held my breath for the first boot.
The system booted, BIOS popped up, the memory check completed, the Windows CD started booting and then it suddenly shut down. My smile went to frown, but I tried to restart it. No go...no BIOS, no nothing. Why? As I found out later, I cooked the CPU because it didn't get any cooling.
I brought the whole build over to a friend's dad, who I should have built it with to begin with but my "more experienced" friend wanted to share the fun, so I let him. Anyway...he checked it out and as soon as he pulled the HSF off he said, "there's your problem". He noticed right away it was the wrong cooler because the bottom wasn't flat (as if the fact that it was so hard to install shouldn't have given it away to me, lol). Anyway, since it wasn't flat the die didn't ever make contact with the sink...no contact, no cool, no CPU, lol. That was a shitty day, lol.
I bought the 1.2 Ghz online and he traded the incorrect cooler for a good one. We rebuilt it successfully once the chip came in and it ran fine for about a year. Then all of a sudden it stopped being able to hold an OS for more than six months without BSOD on startup. No idea why. After that I reinstalled for a while every so often until I tired of it, then it went in the closet, lol. Probably something went quirky after being subjected to that initial tweak when the first CPU popped and it took a while for whatever it was to break down completely until it started causing instability. I dunno...never bothered to figure it out.
Anyway...that whole story brought to you only because "not sitting right" made me think of it, lol. Mine really sat wrong...I suppose yours sat...a little better, lol.