Use cluster test to see if it's battery, alt, or both. The alt isn't a charger, so if you've had a bad battery for a while, the alt could go bad.
Voltage off should be around 12 V and on around 14V.
Your starter isn't an issue at all.
I'm thinking just battery, but you need to check the voltage to begin.
Search Cluster test.
I'm so depressed. No one wants to come see me. :(
Mangofy your E46!