Here is the truth.... bottom line is.....
Your solution MUST improve sales.
Regardless of any other consideration, if you can convince your colleagues that the new solution will improve the selling prospects of your organisation, then you are more likely to get funding for your pet project.
So before you pitch your idea to the board, go to your sales and marketing departments first. Find out what their problems are and make sure your solution can support what they are trying to do. I guarantee that your likelihood of project approval will at least double with approval and backing by sales and marketing.