Save yourself a possible wild goose chase and have a through look at the battery and charging system.
Is the battery good? Does it hold a charge?
Are the battery terminals CLEAN and tight? How about the battery negative? These are bad about splitting if over tightened.
How about the grounds around the radiator core support? Are the clean and tight?
Have the alternator tested for correct output and excessive AC ripple (bad diode). Most auto parts stores will test for free.
Post back when certain the charging system is in tip top shape.