If the starting has not gotten more sluggish over time I would back your tow car next to your genset and with jumper cables hook your starter up directly and see if that makes a difference in how it cranks. If no difference I would suspect the starter, if better I would look first at the cable ends for corrosion especially inside the cable ends(under the shrink wrap). If that looks ok what gauge wire is used from house batteries to starter? The longer the wire the thicker it should be. If ok you know from the tow car test a starting battery will work as someone else already posted.