The Cummins starter, has contacts in the solinoid ; on the side of the starter under the small plate , held on with 3 , 8mm headed bolts, there is a spring loaded plunger with a bronze plate that moves down to contact 2 brass contacts to feed power to the armature. These contacts arc every time the starter is used, so they wear, some times they can be cleaned, most times the contacts need to be replaced.This could be your click but no crank problem , BUT should not bother the radio memory, for that you have a bad connection some where, the radio memory will drop out below 9 volts. Start at the battery and check all your power and ground connections. If necessary have some one turn the key while you look for the problem, wear eye protection, bad connections can spark.
Were you having this problem with the other battery?
99DSDP 3884, Freightliner, XC, CAT 3126B, 300 HP /ALLISON 3060
2000 Caravan toad, Remco & Blue Ox.