I need to exchange motherboard

Yes, you can swap out your logic board if yours is dead.

But, before you go down this path keep in mind the limits of the system and the fact Apple will likely cut off future OS support for it either this or next year. So you will not be able to upgrade the OS or your apps that need the newer OS to run.

Here is the IFIXIT guide you'll need to follow as we don't have an exact match for your system this one is as close as we have: iMac Intel 24" EMC 2111 Logic Board Replacement As for a replacement logic board here are your choices:

• 3.06 GHz, Core 2 Duo - Apple P/N 661-4992
• 2.93 GHz, Core 2 Duo - Apple P/N 661-4993
• 2.66 GHz, Core 2 Duo - Apple P/N 661-4994

As a reference a 3.06 GHz can be gotten with CPU for around $170 US