The alternator will not figure into it until after the car starts up.
1) make sure your new battery is fully charged.
2) If that does not work the check positive and ground connections
-- remove neg connection at battery. Clean the connector and reattach to battery. Trace that negative cable(s) to the other ends. Disconnect those ends, clean the connectors and reattach.
-- do the same with the positive battery cable.
Inspect the cables to see if they have started to corrode inside the insulation. If so replace the corroded cables
Three years is a long time. I let a 65 VW bug set for two years, the points had turned to green powder. I replaced the points, put in a gallon of gas, jumped it and it started right up. Nothing like a simple machine.