I think you can rebuild Harrenhal. Be the Lord of Harrenhal and accumulate 1,000 gold and an event should fire that allows you to start reconstruction. But some bad stuff starts to happen, and I don't know if the "curse" gets worse if you begin reconstruction but I played as Aerion Qoherys right after Aegon's conquest. Aerion died right after I started rebuilding it and all of my children but two died, my eldest son only had one son before he died, and that son ended up dying so his Uncle inherited and then nearly all his kids died. Plus it helps to have your Master of Coin oversee construction in the county, and an event occasionally fires that results in you giving them 200 gold or slowing down reconstruction. And then there's an event that either lowers your health by 2 and gives you the brave trait or give you the paranoid or craven trait. And the process takes generations. It can be brutal.
