If the vectors are open then the vector validator won't show anything as an open vector isn't necessarily an error. If the open vector has overlapping sections giving the visual appearance of a closed vector then the tool will pick up on that.
To join vectors you can use the Join tool as you've tried but you must have the tolerance set to a level that enable the vectors to be closed. If the tool is saying there is an open vector in the selection but the Join button is greyed out then that indicates that the tolerance is too small to bridge the gap. Increase it until the button is active. Once it's joined the vectors be sure to check that they still look the way you expect as large tolerance values can caused joins where you might not want them.
I tend to use one of three individual Join (Straight line, Curve, End Points) rather than the main join tool as I prefer to do the joins one at a time so I can see what is going on.