The CPU is mounted in a Zero Insertion Force (ZIF) socket. If you (gently!) try to pull the CPU out of its socket, you will find that it does not budge. You first need to release the chip from the socket. Turn the screw on the CPU socket 180 degrees counter-clockwise to release the old CPU. Then pull up on the CPU chip to remove it.
https://www.ifixit.com/Guide/iMac+Intel+20-Inch+EMC+2105+and+2118+CPU+Replacement/35350
That’s just the CPU. That’s not the chipset. The chipset includes the bridge chips and such; they are soldered to the board. Only the CPU is socketed. Swapping the CPU will not solve the problem.