Not to sure I know what you mean, are you saying that clicking "Continue" will make the game start all over again? with the opening cinematic and everything?
If this is what you mean then once you start the new game try to load the save that you want from within the game and not from the main menu.
If this isn't what you mean then I was reminded of an old trick that would work in Fallout 3, on the main menu click "New" to start a new game, after all of the cinematics go to the menu and load an old save.
It is possible that your most recent save has glitched and will require you to load a slightly older save.
Hope this helps.