Question: After a star lives and dies, I assume virtually all of its mass would be photons. If enough stars have already lived and died, couldn’t there be enough photon energy out there to account for all the "missing mass" (=dark matter) in the universe?

And if there were enough photons to account for all the missing mass, what would it look like to us?

Answer: 
As a general rule, zero mass particles which travel with the velocity of light are not good for dark matter, because [dark matter concentrates](http://en.wikipedia.org/wiki/Dark_matter_halo) around gravitational attractors. It has to be particles with some mass that can be at rest in order to stay around a galactic center from the beginning. In addition they have to be controlled by weak interactions, if they decay, because the dark matter halo is stable for long periods.

Maybe I should add that very cool photons from the beginning of the formation of the observed universe exist and have been detected as [Comsmic Microwave Background](http://en.wikipedia.org/wiki/Microwave_background_radiation) radiation, very low frequency photons, uniformly distributed in the cosmos.
Photons don't have mass. So your assumption's incorrect, although I don't know how much of a (say) main sequence star's mass gets converted into photons over its lifespan. 

Photon's can't account for, say, dark matter, because *dark matter has mass*.

Thermal energy (in the vacuum) is comprised of photons, which can spontaneously form particle-antiparticle pairs. Usually these quickly annihilate, so this is also not a good source of mass.