11.6v is very low, especially during winter. Could just be that it's cranking slowly, also the fuel pump prime might not be getting the pressure high enough with a low voltage prime.
Check the battery voltage with the engine idling, should be about 14.4v. Showing the alternator is ok. Then shut the engine down/ignition off and monitor the battery voltage. It will probably show 12.5-12.8v at first, then very slowly drop back to 11.6. Showing your battery is toast.
Could also charge the battery over night, or get a jump start in the morning to see if it starts easier.