Same here, I have reset the phase several times, logged out and back in, but nothing seems to change it. The quest seems broken.
I have done some trolling on this and found in the past it was resolved by resetting the phase from the Fleet, so I travelled there, reset everything, flew back to the Corellia Orbital Station, had to click on the Firejawk again which generated the cut scene of my escape pod leaving and going to the Tyrant again - but when on the Tyrant exactly the same thing happens.
Everything greyed out, quest not working. I think we will have to wait till someone hears from Bioware on this one.