I can't install things via YaST using rpms, YaST sources, or YOU anymore. In each case, it will tell me the installation attempt has failed, with the following diagnostic message:

ERROR(InstTarget:E_RpmDB_subprocess_failed)
---
error: db4 error(-30978) from db->close: DB_RUNRECOVERY: Fatal error, run database recovery
rpmdb: PANIC: fatal region error detected; run recovery
error: db4 error(-30978) from db->close: DB_RUNRECOVERY: Fatal error, run database recovery
rpmdb: PANIC: fatal region error detected; run recovery
error: db4 error(-30978) from db->close: DB_RUNRECOVERY: Fatal error, run database recovery
rpmdb: PANIC: fatal region error detected; run recovery
error: db4 error(-30978) from db->close: DB_RUNRECOVERY: Fatal error, run database recovery
rpmdb: PANIC: fatal region error detected; run recovery
error: db4 error(-30978) from dbenv->close: DB_RUNRECOVERY: Fatal error, run database recovery

What can I do to "run database recovery"? Hopefully, this can let me update my system for security patches soon.

OK, sounds as though your system is in a pretty broken state. I think, as root, u need you to rebuild your package database by running the following in a shell:

rpm --rebuilddb

I would like a second opinion on this....

I think the above is the way to go. You will be on the safe side if you backup /var/lib/rpm first.
http://portal.suse.com/sdb/en/1999/01/ke_rpm-db.html

Yes. rpm --rebuilddb is correct.

Thanks. It fixed the problem.