I haven't tested this code yet because it's Saturday but this should get you on the right track...
In the file include/staff/newticket.inc.php replace the following select item starting at line 58
<select name="deptId">
<option value="" selected >Select Department</option>
<?
$services= db_query('SELECT dept_id,dept_name FROM '.DEPT_TABLE.' ORDER BY dept_name');
while (list($deptId,$dept) = db_fetch_row($services)){
if($info == canAccessDept($info)){
$selected = ($info==$deptId)?'selected':''; ?>
<option value="<?=$deptId?>"<?=$selected?>><?=$dept?></option>
<?
} }?>
</select>
I have added a query that will return if the staff member can access the department, if the query returns false the staff member shouldn't be able to access it.
The reason I put it in place like this is to ensure it doesn't affect people with access to multiple departments.
This is off the top of my head and if it doesn't work let me know as I have some similar code in production and I can fix it later today easily if there is a problem.
Actually let me know how it goes either way