K.I.S.S.
The battery that came with my (just purchased) '70 Charger shows 12v resting, and on the NoCo pulse charger it shows 100% capacity. But the car lived in Florida all its life and is now in the below-freezing weather of Maryland.
Turn the key, CLICK. And that's it.
Swap in a battery from my '91 Daytona, starts right up.
Check standing voltage in your battery. If you have a battery tender (EVERY classic car guy has some sort of battery maintainer, right?), hook it up and wait for the green light. Try again once it says fully charged.
Just because you have volts, doesn't mean you have AMPS, and amps are what start a car. Think of a water hose - you can have "water" trickling out of the hose (volts)...or you can have full-bore, knock-over-a-horse fire-hose water pressure (amps).
Swap batteries with something else in the stable, and see if it starts. If the battery is bad, you will not get a valid test reading - you need to test charging system output levels with a good battery.
I strongly recommend the NoCo line of battery charger/maintainers. I have used BatteryTender units on my motorcycle batteries for years, but they will only float-maintain a good battery. I have had stone-dead batteries brought back to life by NoCo chargers. $40 at WallyWorld. They also make some bad-*** pocket-size jump start power units. The only catch with them is, you may need to hook a jump box to a stone-dead battery long enough for the charger to register "hey, there's a battery here" and start the charging cycle. Usually 2 minutes will do it.
I'm guessing you need an alternator, and a battery. A running 11v is too low, and depending how long it has been run like that you could have damaged a cell in the battery, knocking down its effective amperage. Again, though - put in a known-good battery and re-check voltage at idle, and check for climb with revs.