Hi Frost
Let me try to help you with this situation, all motherboards has Internet Adapter (Physical one) But sounds like you're talking about non-physical internet adapters a.k.a Internet drivers. I want to ask 2 questions from you.
1. Did you re-install the windows OS ?
2. What OS you use (win7 , win8, etc.) ?
For now you can install Internet Adapters by using a USB, first download internet adapters to the usb from a computer that has working internet, then insert it in your computer with the new motherboard, and install the drivers.
If you installed windows properly, it won't ask for internet adapters. (when windows not installed properly, it ask for many drivers)