Unfortunately your recovery options are pretty limited, because the randomly-generated password for the server's database is stored in an encrypted section of the registry (in what Windows calls local machine secrets database). Getting that data back from a non-bootable system is
really, really hard, to the point where it's better to spend the time just rebuilding a fresh database.
As long as you get the server's identity key files
pubkey.crt and
privkey.crt, and you load those into the replacement server, the clients should reconnect to the replacement server and reappear in its console. You'll have to rebuild the task definitions and any custom inventory queries from there on, but since you'll probably be able to recover the image files and such from the old server using BartPE.