Here "equipment" refers to the sailors' equipment needed to sail the ship: tackle, hoists, beams of wood, block and tackle, ropes, lines, sails, and the like. This indicates how desperate the situation was.
# When the sun and stars did not shine on us for many days
They could not see the sun and stars because of the dark storm clouds. Sailors needed to see the sun and stars in order to know where they were and what direction they were headed.
# the great storm still beat upon us
"the terrible storm still blew us roughly back and forth"
# any more hope that we should be saved was abandoned