Edit include/staff/newticket.inc.php around line 70ish
Replace This:
while (list($deptId,$dept) = db_fetch_row($services)){
$selected = ($info==$deptId)?'selected':''; ?>
<option value="<?=$deptId?>"<?=$selected?>><?=$dept?></option>
<?
}?>
With This:
while (list($deptId,$dept) = db_fetch_row($services)){
$selected = ($info==$deptId)?'selected':''; ?>
<?php if ($thisuser->canAccessDept($deptId)){ ?>
<option value="<?=$deptId?>"<?=$selected?>><?=$dept?></option>
<?php } ?>
<?
}?>
And then in the admin panel > Staff Tab> Click on User Groups and then select the group that your user belongs to (ie Staff). Uncheck all of the departments that are listed under Dept Access.