Sick Greenfinch?

In our garden this morning, lethargic & dishevelled it allowed me to approach within a couple of metres before fluttering off to a nearby bush.Would this be "the" virus that affects them? we had a similar Chaffinch a couple of months ago which later died, though our resident small flock of House Sparrows seem to doing OK but they eat more suet pellets. We did have masses of Starlings that emptied the feeder in minutes in the Winter but only one dead one - sniffed out by my dog - buried deep within a Conifer bush. would they carry any kind of  disease that transmits to other species?