Sorry, I probably shouldn't have said that I have it exactly like the original poster. However, I got the basically the same symptoms.
I only had MySql already installed on my machine. Everything else I either downloaded (JDK1.5) or it came with the bundle already (Tomcat). The Tomcat installation already had the JConnector class in the directory (specifically; C:\alfresco\tomcat\common\lib).
I've checked MySql and was able to log in as the alfresco user. Queried for table and got an empty set. Is there, perhaps, a port on the MySql server that Alfresco is looking for? I.e., I recall a port selection being something to the extent of 3306 as default. Although I changed my to 3308.
Other than that I'm not quite sure what else it could be.
Thanks,
-dl