Excel will look into your regional settings and see how a date should be formatted and only if that matches, it will automatically format your cell as a date.
So if you have set your regional settings to use a date as dd-mm-yyyy (note the -), an output where / is used will be ignored.
Additionally, it may be the case that the cells have a ' in front of the date. This character will basically instruct the cell to always be a string. This is something excel could've done during an import.
First thing I would do is change the regional settings to american date so it has / and try to load the spreadsheet again. Selecting the entire column, chosing right-click->Format Cells, and set it to Date should now work.
Once it is succesfully converted to a date and you saved the sheet, you can change back your regional settings.