Well, if you have no cronjob in cpanel, then you not use cron.php
If its used you would have a cronjob + $CONF['cron'] = 1; in settings_sql.php
No manual reset, and wouldnt help you out. Your issue is with week and month of some sort, so nothing is minutely reset would change
Besides, how did you know your stats reset? Do you made use of the template tags to show hits in? If so are they still using weekly? {$unq_in_0_weekly}