If you could clutch start it immediately when towed/pushed it's probably not fuel. A decent test for this w/ a mechanical IP (If it's electronic look for how to prime it some other way) is trying to start it w/ the pedal to the floor since that's the fastest way to prime the fuel system if it's lost pressure. Barring fuel I'm guessing it's cranking speed/glow plug function. Glow plug function does not strictly correspond to the indicator light function IME, but it could be different for different vehicles so you'll have the check. Determining if the GPs are good shouldn't be too hard, just
check the voltage/current for whatever values the Fiesta has. Take the battery inside so it's warm before starting to see if you can get a large enough increase in current to raise cranking speed sufficiently to start it. If a warm battery doesn't get it started and the glow plugs are good I would try synthetic oil since it's cheap to see if that can help out enough w/ cranking speed to start it, and/or putting another battery in parallel if you can get a used one for cheap.