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...Well... Sean Connery+Submarines sounds like The Hunt For Red October. Is this it, and you're mixing up two films? Because, if it's not, I'm sorry for wasting your time. ^_^
Edited by loracarol
I have seen a film where some older retired military guys get involved in a hare-brained plot to distract the enemy. It was set in WWII but made later.
Another possibility due to the mention of the Cold War could be "The Russians Are Coming, The Russians Are Coming!" A New England town thinks there is an enemy submarine off their shoreline.
"You want weapons?! We're in a Library! BOOKS! The best weapons in the universe!" — The Doctor
I think it might be the 1954 film Hell And High Water.
Here is the IMDB summary: "During the Cold War, a scientific team refits a Japanese submarine and hires an ex-Navy officer to find a secret Chinese atomic island base and prevent a Communist plot against America that could trigger WW3."
It stars Richard Widmark, not Sean Connery.
Film with I think Sean Connery in it about some WWII veteran submariners having a re-union on their old submarine. They all go mad and try to attack Russia. In the end everyone except for the captain escape and the submarine sinks.
It had a bit where the main character explained what a cold war was to his friend.