By all means check the whole car over, but first check the battery.
1) If a hydrometer shows all cells are even and reading 1270 (fully charged) then check main connections, and starter motor. No need to rebuild the generator its working fine the Hydrometer said so.
2) If the Hydrometer shows all cells are even and reading low. Look for slipping belt or faulty generator/regulator/cutout. Or a current draw.
3) If the battery is stuffed it will have uneven specific gravity readings on the hydrometer irrespective of age. This means two cells showing charged and one showing flat then the battery is cactus. This shows that because two cells are charged then it must be..........charging......yes. One cell flat.....its not accepting a charge...........fault cell.
If you have 2 or three, put the battery on charge over night and recheck with the Hydrometer until all cells are charged.
By just cleaning and replacing things will not identify the problem. It may get it going but you wont know why.
If you would like to check the power circuit and earth circuit for voltage drop that's easy too. If people are interested sing out
This stuff is Auto Electrical 101 for 1st year apprentices.
If I checked a car or truck in any other order than this my boss would have flipped. If one of the young lads did this where I work now he would get his butt kicked all over the workshop. I wonder how a customer would feel if I said we rebuilt your starter generator, regulator, cleaned all the connections, then found you have a faulty battery, but its now fixed.
Labor $350
Battery $80
Regards Ross