Q: I received a new logic board and now my computer has no serial number under 'about this mac', and I need it to submit questions to apple.  What do I do?

You can open System Profiler and see if it contains your serial number.

Or have the computer near a previous connected Wifi or on a Ethernet cable to your router.

Reboot holding the D key down for like what would appear to be 10 minutes until Hardware Test appears on the screen.

You can run a test if you wish.

There is a pane at the top if selected will give you your new serial number.

You also can use Terminal

You can quickly retrieve any Macs serial number via the command line by using the following command string:

 

system_profiler |grep "r (system)"

 

The command results will look something like this:

 

$ system_profiler |grep "r (system)"


Serial Number (system): C24E1322XXXX

If that fails you can give them your MAC address which is unique to each machine and there are records at Apple with it.

Open Utilities > Terminal. Copy, paste and press enter:

For your computers Ethernet (wired) MAC address: ifconfig en0 | grep ether

For your computers Airport (wireless) MAC address: ifconfig en1 | grep ether

After my logic board was replaced by an AASP, he failed to register it which associates it with the serial number. I called Applecare and was told that a special tool/USB type dongle was needed for this task (which the AASPs have) and the AASP returned to register it with Apple. So, I'd contact Apple and/or whomever did the work and tell them that they need to register the new logic board with Apple's servers. Even if you can get the serial number using above suggestions, the logic board still needs to be registered.

Depending on how old it is, the serial number sould be on the bottom of the case (2009 and later models), or inside the battery bay (2008 and earlier).  

See MacBook Pro: How to find the serial number.