I had the logic board in my MacBook Pro replaced under AppleCare warranty recently with fantastic service from the Regent Street Apple Store. That was all good. However when you change the logic board in a mac some things can go awry.
The key thing that changes is the ethernet MAC address of the machine. This is the low level network identity which is used prior to getting a proper TCP/IP address for use on the internet. They are (I think) unique per machine and so they are used as a key for all sorts of things. Two I have found so far are Time Machine and MobileMe syncing.
Neither of these services warns you, they just stop working, which is quite irritating. To fix Time Machine you need to reselect the drive you are backing up to, this should work, but didn't for me.
For MobileMe you need to go to the Sync tab in the MobileMe preferences and tell it that the old machine name is really the same as the new one. Then you'll get to merge the data.
It is a pity that macosx doesn't recognise that it has a new motherboard and offer to fix these for you, but hopefully this list will help you one the right path to getting things back to normal.