Who's server? Yours? Company or host? If it is a company server, I seriously recommend that you urge your organization to update their MySQL, security improvements alone make it worthwhile. While they are at it, how about their PHP version? v5.3.3 is out (and I seem to recall seing a PHP v6.x being spoken about, but I am not sure what this is or when). Any organization really needs to make sure that these things are either current or near current or are updated regularly, at least annually. If it is a hosted situation, I would suggest that you run, as quickly as you can to another host, as the host is not doing the right thing by its clientele.
Now for the really bad news... Support for Moodle 1.8.4 has been discontinued as of last December I believe.
You also have me baffled, you talked about MySQL yet the error you wrote about Item MDL-8159, was a duplicate of MDL-8160 and that relates to Oracle and PostGreSQL environments, not MySQL. There is no patch as far as I can tell, and that means you will have to change the query, which means you will have to find it. So, are you sure the DBMS is MySQL?
Or perhaps you can update to Moodle 1.9.11, which might actually be easier, after your DBMS is updated. Or if you are really new, and have no courses at all, then go to v2.0.x, which is really very good and a great place to be starting from if you or your Users have not used Moodle before.