|Your company's promotion policy sounds like it was designed to promote dissatisfaction. People should be promoted on the basis of merit, and not because they happen to be in the right place at the right time. That type of promotion strategy makes the whole process sound rather random.|
Management in your company practically admitted there is no rhyme or reason to their decision-making when they offered you compensation instead of a promotion. They were essentially saying, "It could have just as easily been you, so here's some money." And then to top it off, your raise now resides in the wasteland known as the president's desk.
You should not wait any longer. It has been six weeks already, and people tend to forget these kinds of commitments, particularly in a company with such a loose raise and promotion policy. You should ask your manager if your raise is going to appear in your next paycheck. If you hear anything other than "yes," you should work your way up the ladder until you get that "yes."
If the company continues to give you the runaround, you should start to look around.