They were close to the coast. Couldn’t they have fished?
By the way, just how often do those droughts occur?
Regarding fishing, that's a rather salty diet. Their problem was fresh water ~ not fish; but game was in short supply; the Indians had moved upstream for fresh water and were a long way away from Jamestwn.
Little went on in the East Coast area until about 1620 ~ and then settlers came to many places, indians attacked, etc. Europe prepared to plunge into the 30 years war ~ just all sorts of stuff.