Aromatization in polycyclic systems is a little unusual - these systems tend to behave as if they were made up of discrete benzene rings, with resonance forms made of all the different ways of isolating discrete benzen rings in the system. Your anthracene, for example, could act as if any one of the rings was a benzene ring, with the other two rings being cyclohexadienes. The aromatic character in each ring is much less than if it were three separate benzene rings, and the possibility to form two isolated benzene rings is part of what drives the center ring to be reactive to Diels-Alder reactions. (See Clar's Rule for aromaticity of polycyclic aromatic hydrocarbons).
As for the melting point, as orgopete says, instead of melting you are decomposing the adduct. Look at your components - p-benzoquinone melts around 115C, anthracene around 215C - I don't know what temperature is required to drive the retro Diels-Alder, but you can see how you might have some liquid p-benzoquinone, some solid anthracene, and some of your adduct for a very wide range of temperatures. This is not a melting point.
DSC may be able to give you some numbers for the temperatures at which these transitions occur, but if the retro Diels-Alder is occurring at a lower temperature than the melting point of the adduct, then you simply can't determine a melting point for the adduct, only a decomposition temperature.