Get a can of Aerostart (you can also use wd40, hair spray, undie arm spray as last resort) start her up, when she faulters, give a light spray into intake, if she picks up and runs on the spray, and then faulters when you stop the spray - its a fuel problem. If it faulters on spray then it could be electrical.
If you are running original points (kettering sytem) check gaps and points condition (no pits or holes, splats).
Check capacitor, no cap = no ignition. Best way to check is - get a new one, I dont know many in the club who would have a metre to check caps.
when spraying etc, keep all your bits away from intake esp face, eyes etc
If its starting, then battery will be good enough, for the alternator to stall a motor it would require a near dead short, and "the smoke" would be a good indicator.
I love a good suduko.
( I once had an English car, the cap was screwed onto the moving base plate in the dizzy, came loose, & as it rattled around the ignition splatted on and off. I could not find it as I did not appreciate the importance of the cap, I end up making up & fitting CDI and only then did I see the loose cap.)