Here is my two long cents!! When I get something done that I found annoying I always try to help by writing out a longer guide for the next guy... yeah, I know, saint.
While deep cleaning a computer ended up pulling the large heatsink off and then finding that the heatsink took the processor out due to some commercial style glue used. Of course, this mistake ended up costing me a bunch of time. The large heat sink would not allow me to put the processor back.... see the arm couldn't be raised BECAUSE of the heatsink size; therefore, you can't reinsert and do as others suggest and twist it to break the hold while still in the socket; therefore you've got to separate the two using other means.
O.K. every you turn they say "twist it"... some will say blow dryer use and some will say a "Artic Silver cleaner" (which appears to be isopropyl alcohol with a new name) but all I ended up having was my hands hurting. I got so worried that I started thinking desparate like cutting the arm shorter on the socket which would give me the clearance needed to push the arm down and then finding adhesive putty to adhere the cut down arm down (I KNOW, I KNOW, VERY BAD IDEA but it might of worked?!?) or chiseling on the chip which likely would have ended with a pretty piece of silicon. But see this thing was stuck!!! It was so stuck I even got confused as to where the chip ended and the heatsink began... I had to google a picture of a Socket 939 processor to clear that up.
If yours twisted right off then it was likely just compound not this epoxy like glue I encountered.
So using the above suggestions I gathered a couple of items: 91% Isopropyl Alcohol, bowl, small knife, a box knife's razor blade (essential), blow dryer, towel, and hammer (!!!!!). What follows is what worked... I'm not counting the steps of twisting and heating and twisting that didn't do anything.
1) I used the box knife razor blade and carefully trimmed all the excess glue all around the chip.
2) Filled bowl with Isopropyl Alcohol and gently put chip in keeping pins facing up in the bowl to protect them the best I could (this means you might need more than one bottle of alcohol based on your bowl)
3) Let sit over night in Alcohol. I don't actually know if the alcohol did anything because obviously the glue beyond the edge of the chip might not have been effected at all... but it was part of what I did to get the final success of the thing.
4) Remove from alcohol and set heatsink on towel chip up... Blow dry the hell out of it... I actually propped the blow dryer so it could run a few long minutes getting it nice and hot. I made sure that it blew on both chip and the copper backing of the heatsink to make sure that it softened the glue in between. It got hot... hot enough that I couldn't handle it with bare skin (means it was over 113 degrees). I looked it up, the chip can operate at a max range of 155 degrees (70 Celsius) so without electric current it probably has a damage point at a really, really high temperature. So I am guessing that a blow dryer won't hurt it.
5) Twist it off using towel to hold heatsink and fingers to twist chip. See that should have worked right? Well, mine didn't come off and trust me I put some grunting effort into it SOOOOO now is the time to grab small hammer and beat the hell out of it!!!! Just kidding, but do grab the hammer if it didn't work for you too.
6) While still hot and softened from alcohol. I took a small hammer and box knife razor blade. It looks to be the ideal tool. It has a small razor blade edge and rigid steel body. It is as long as the chip so it will conceivably apply and even force along the whole chip when tapped. I positioned the blade so that it was at the meeting the point between the chip and heat sink (angled some to make sure the blade edge was at the exact point) and then very lightly (!!) tapped the blade and pop off it came off.
7) We all know not to touch the pins... keeping the oils of our fingers off etc... but if you twist and twist you've bent some pins. I found that using the box knife razor blade and inserting it behind first row of pins gave room to use another small knife to straighten those pins. Also used the box knife razor blade as a pry to gently line up the whole row of pins. Taking my time I was able to gently align and try, align some more and try until it (with no force) went into the socket again.
"Arctic Silver Thermal Adhesive is a permanent adhesive. Components you attach with Arctic Silver Thermal Adhesive will stay attached forever." But with the trimming of excess, softening with alcohol, and heating to reduce its effectiveness it just might take a small blow to break the adhesive strength of the thing.
Take the above knowing that it came from an idiot who shouldn't have pulled the heatsink out in the first place since a liberal amount of compressed air would have done the trick. I've been amateur building computers and repairing since 1990 and I inadvertently turned a simple job into a nightmare but hopefully yours ends well like mine. Good luck.