Sorry for the late response. Your log file shows this message:
<message>You have an error in your SQL syntax; check the manual that corresponds to your MySQL server version for the right syntax to use near 'type=innodb' at line 11</message>
…which suggests that the MySQL instance you are using is not using a database type of innodb. You can change that in your MySQL configuration.
It is difficult to figure out what is really happening in your environment, though, because there are so many ways to set up Unix-like systems.
As for your troubles using hsqldb, I looked back at your error message that read:
java.io.FileNotFoundException: /purl.lck (Permission denied)
Did you happen to check to see if that file was actually present, and what permissions it had?
I have checked a couple of Linux machines running the current version of PURLZ, and I don’t see either of these problems. I suppose you might run into problems with a version of Java more recent than 1.6. Can you check your Java version (by running ‘java -version’) and let me know what you see?