Whatever appropriate "fair use" is, I'm pretty sure it isn't build your brand around it, and if you license a composition for use in a regional radio ad in order to avoid royalty payments, it's not fair use to also use it for everything else, whether it's 3.5 seconds long or not.

The Intel jingle is only four notes, but Walter Werzowa's done rather well out of being paid to compose variants of it and it's rather more famous than his actual records...