I suggest to team up with your boss. I see nothing in your post that makes me assume that there is any conflict between the two of you; and I assume that your boss is truthful in that he simply has no way to influence the situation. I am in a similar situation (large company, involved processes regarding salary management once a year with no particular power on my side; a general "don't talk with terrorists" approach; and exceptions handled through another process once every 6 months if at all), and *I* would not be able to influence your salary in a realistic manner (and even if, I could not promise you anything about it up front).

As your boss probably has no reason to actively get rid of you, simply talk to him in a good-natured way. Make no promises or threats; simply tell him what you told us. Make it non-whiney and matter-of fact; just so he is aware. In fact, I guess you already did that. Do not tell him that you are looking for a new job.

Meanwhile, go look for a new job. Take the opportunity to find one which might be more interesting, more worthwhile, maybe so you have a shorter commute etc.. As soon as you hold your new contract in your hands, hand in your resignation, never the other way round.

In my experience, there is very little an employee can do about his salary, after signing the contract. Bosses normally know perfectly well about the salary structure of their company (i.e., how much a person of skill X is "supposed" to earn). This may be different in small startups and the like, but large companies have processes etc. in place, and often have other gratification/gamification mechanisms in place than the yearly salary raise (or they better should have...). So you have little leverage there, as an employee.