Q: mother board replaced, issue with OS X

Who replaced it? If it was done at an Apple Authorized Repair Center call them back immediately.

I would check the connections and make sure you didn't get a damaged board to begin with or if some cable is not entirely connected, or bent, borked, crimped or broken, or misaligned, or that you don't have a torx screw laying around that needed to be put back or you put the wrong length screw in the wrong thread or you fried something due to improper grounding or the CPU has too much thermal grease, too little thermal grease, or just enough thermal grease but you stuck a thermal pad on there as well and are slowly and horribly killing it. There is only one way to replace a logic board but there are also a million ways not to.

Are you trying to boot normally with the existing OSX installation?

Can you boot to Recovery?

About OS X Recovery - Apple Support

Try both from Recovery partition and Internet Recovery

Do you have access to another Mac?

What does DIsk Utility show about the disk?

Maybe:

http://www.tomshardware.com/answers/id-2714286/locked-recovery.html

On the other Mac download the El Capitan installer from the Purchased section of the Mac App Store and make a bootable USB device using:

http://liondiskmaker.com/

Then try booting the problem Mac from that and try installing OSX on the interna disk

The El Capitan installer is what one downloads from the Mac App Store to upgrade to El Capitan

It is in your Applications folder with title: Install OS X El Capitan