Hi R.,
In the most respectful way, I would talk to HR and simply ask why employees in your department are not eligible to apply for better positions within the company. What doesn't make sense to me, and I have worked in HR for very big organizations, is why? In most cases, employers want to see employees stay in their original positions for at least one year. During that time an employee's performance can be fairly evaluated. If the evaluation is good, there should be no reason why they should not be able to advance to another department or position.
If you don't feel you get a satisfactory answer, then you should privately contact the Labor Board. Keep your job, keep your pride, but do your research quietly.
Blessings......