SMD desoldering - struggling to get this chip quik stuff working, what am I doing wrong?
Be aware that old motherboards have crappy solder that's been sitting under a pile of dust for a long time. Sometimes I find that old solder like that doesn't want to melt. Before using the chipquik, I'd recommend using some flux and fresh solder to tin the old solder, so that it will melt much easier and accept new solder better. If you're crafty you can remove the old solder with solder wick/braid and tin with new solder.

I've never actually used the chipquik for removing chips, so I won't try to help you there, but I can get most chips off easily enough with my Hakko FX888-D and the standard T18-D16 chisel tip (a very small chisel) at 750F. Using a hot air station is definitely easier, but those can get quite expensive for a good one (my Hakko 810B one runs around 800$ new). For the hot air gun I find it easiest to use solder wick to remove as much solder as possible, then use the air gun to heat all sides evenly till it pops off. I definitely recommend investing in one (they come at a decent price from China that should work good enough).

But you are using a soldering iron. I'm sure some people will crucify me for saying this but I if I have a stubborn chip and no hot air gun, sometimes I'll use a razor blade to help lift the chip off the board. First I apply flux to all the leads of the chip, then add a decent amount of solder to 2 of the 4 sides. I then gently maneuver my razor blade under the corner joining 2 sides and run my soldering iron with a good ball of solder up and down both sides, switching as quickly as possible. Once it's heated up enough, you can twist or lift the razor blade very gently and it will begin to lift off both sides. Then you can get the blade further under the chip, remove excess solder with wick and continue the process. Obviously this method runs the risk of damaging traces underneath the board with the razor blade, so use extreme caution. You can usually tell if the area is trace free, and also you don't need to use much pressure at all on the blade if you properly heat the chip. I've also seen a guy use a dab of CA and bond a wooden dowel to the chip, and use that lift the chip off. It's a hack for sure but will work in a pinch. Good luck with your chip removal!