If your mother board died, it could have taken down any of the other components in your PC. Some components might appear to work at first but stability might be an issue. (e.g. faulty ram will cause random BSOD in windows).
Depending on the damage, you may need to consider updating the components as you determine which have failed.
Be sure that the new motherboard works with your processor. Once you replace your motherboard, hopefully you will get a successful beep and a happy boot into windows or whichever OS you are using. If not, then its trial and error from there.
Check the mother board manual to understand the beep tones. There is usually a list.
If you have connected everything correctly, yet when you power up the system, only the lights and fans turn on, but NOTHING else happens, then its likely the CPU has blown, or the mother board does not support the CPU.
Apart from that, just follow the beep codes on start-up. Once you get windows loaded you can find hardware test apps to determine if any component is compromised.
***Whenever you remove the CPU heat sink, always clean the CPU and reapply the thermal compound***
Good luck with this. I hope the damage is not too severe.