An alternator will not "recharge" a battery unless you run it for several hours, not minutes. What is the terminal voltage at the battery posts while the engine is running, and what is the specific gravity of the battery acid? I'd suggest hooking up a low-rate battery charge overnight, maybe 10 amps or so, then checking the specific gravity of all the battery cells after several hours of real charging. They should be between 1.265 and 1.300, and all the cells should test within 15 to 25 points of each other. Once the gravity is up and close to equal, do a high-rate discharge test where the battery is loaded to 1/2 its cold cranking amp rate for 15 seconds. At the end of the 15 second test, with the load still applied, the terminal voltage should be 9.6 volts or more. Until you have done ALL of these tests and completed them successfully, you don't know if the battery is good or not. Once you have established that the battery is good beyond any doubt, then you can move on to checking the alternator and the rest of the circuit. Test one thing at a time. The shotgun approach accomplishes nothing, and just frustrates you.
If you're unable or unwilling to do the right type of testing, let a professional take over. You're wasting your time otherwise.
Jerry
