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: 
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.
It is accepted that the early state of the universe was mainly radiation, then we had expansion; radiation cooled down as a result, and condensed into matter. The pressure of a photon/radiation gas is positive and given by an equation that resembles the universal gas law; PV=.9 NkT (<https://en.wikipedia.org/wiki/Photon_gas>). 
So by logic, the total(equivalent) mass or the total condensed energy in the universe, must be less than the total radiation at the start. If also the condensation process involved only a small portion of that radiation, then surely we should have plenty of radiation left uncondensed- and could easily be much more than that of all matter. This remaining gas is continuing its expansion of course- today and in the future.Since momentum levels follow energy levels for photons, there must be plenty of momentum around too- due to radiation that is exerting pressure on the various matter objects, producing some expected and may be not so expected situations. If we accept this point of view, one can do detail calculations to get the full picture. The rate of expansion could be one useful result to compare with present data.