since the form HPD:Help Desk is part of the deployable applicaiton "Remedy Incident Management" you'll have to map your new permission group to a role first. This is done in User Tool with the "Roles" form.
So create a new entry in the Roles Form:
Application Name: Remedy Incident Management
Role Name: Incident Reporting (or similar)
Role ID: -1234 (I'd use the negative number (group id) of the new incident reporting group
Test: Group Name from Group Form
Production: Group Name from Group Form
After that you can set the Role (permission) on the corresponding navigaiton item on HPD:Help Desk.
Users are still given Permission groups, not roles.
So you'll have to put the Group "Incident Reporting" or whatever you've called it (defined in Group Form) into the users group list on the User form. ARS will than automatically map the corresponding role (used within the deployable application) for you.
What about the Report link that you get within the Application Menu of Version 7.6.3 and higher? Not sure what version of the product that you are using, but you would have to restrict the users from getting access to all of the links from all of the consoles - Change Management, Incident Management, IT Home Page, etc. Pretty much you are dealing with an extensive customization requirement that you will have to perform.
You could go into the Report Form and change all of the permissions of the Reports from Public to a specific Permission group - this can be a computed or regular group - does not require a role - and limit accesses this way. However, you would have to monitor this process or build workflow to change the Permission field from Public to the specific group when a record is created.
Just another thing to consider.
Hope this helps?