The OS would not normally be linked to your serial number, so I would not expect this to be the situation. Do you happen to have FileValue enabled (encryption)?
What indications were you getting that the board was going bad? Is it possible that you aren't typing the password that you think you are, and have a bad key from liquid damage? I would type the password in a visible space just to verify.
I would boot the laptop from an external bootable volume, which will allow you to see your internal drive as a secondary drive and get at your data, etc. You can do this by connecting an external drive and powering on with the option key held down, which will display the boot options...I would be curious to see if you do get the boot options and not a padlock (which indicates a firmware lock on the new board). Boards with firmware locks can behave in strange ways, so I would want to rule that out.
Another idea is to follow these instructions and create a new admin account:
https://discussions.apple.com/thread/4328284?tstart=0