You can turn on MySQL's logging by editing your my.cnf. In Linux this is probably located in /etc/my.cnf or /etc/mysql/my.cnf. In Windows it will probably be in C:\Program Files\MySQL\MySQL Server #\my.ini. (where # is the version number)
Add or edit the following:
log-error=/yourdirectory/yourerrorlog
Obviously change the /yourdirectory to where you want the logs. and change the yourerrorlog to what ever you want to call them. Some additional logging options are:
log-bin=/yourdirectory/yourbinlog
log=/yourdirectory/yourgenerallog
log-slow-queries=/yourdirectory/yourslowquerylog
Out of vague curiosity when you setup the username/password what did you grant it for privs?
