Your code contains a number of errors, which is why it isn't working. (I don't think the submit event is even being bound to the form, because your jQuery selector doesn't look right: it should be #form or .form)
Here's a working solution:
HTML
<form id="form" action="destination.html">
    <input type="file" id="filePicker" />
    <br/>
    <input type="submit" value="Submit" />
</form>
JS
var _URL = window.URL || window.webkitURL;
function isSupportedBrowser() {
    return window.File && window.FileReader && window.FileList && window.Image;
}
function getSelectedFile() {
    var fileInput = document.getElementById("filePicker");
    var fileIsSelected = fileInput && fileInput.files && fileInput.files[0];
    if (fileIsSelected)
        return fileInput.files[0];
    else
        return false;
}
function isGoodImage(file) {
    var deferred = jQuery.Deferred();
    var image = new Image();
    image.onload = function() {
        // Check if image is bad/invalid
        if (this.width + this.height === 0) {
            this.onerror();
            return;
        }
        // Check the image resolution
        if (this.width >= 400 && this.height >= 400) {
            deferred.resolve(true);
        } else {
            alert("The image resolution is too low.");
            deferred.resolve(false);
        }
    };
    image.onerror = function() {
        alert("Invalid image. Please select an image file.");
        deferred.resolve(false);
    }
    image.src = _URL.createObjectURL(file);
    return deferred.promise();
}
$("#form").submit(function(event) {
    var form = this;
    if (isSupportedBrowser()) {
        event.preventDefault(); //Stop the submit for now
        var file = getSelectedFile();
        if (!file) {
            alert("Please select an image file.");
            return;
        }
        isGoodImage(file).then(function(isGood) {
            if (isGood)
                form.submit();
        });
    }
});
isSupportedBrowser() makes sure that the user's browser supports the required functions before attempting to check the image.
getSelectedFile() makes sure the user has picked a file, and then passes the file data back.
isGoodImage() takes the file data and attempts to construct an image element from it. If onerror is fired, it's not an image or is a corrupted file. If onload is fired, it does a sanity check to make sure the image has valid dimensions, and then validates that the resolution is above 400x400.
Since onerror and onload events are fired asynchronously, the function needs to pass back a promise indicating the result of the validation.
Finally, the submit handler on the form ties all these method calls together and only allows the form to submit if the resolution check comes back good.
Link to fiddle: http://jsfiddle.net/uwj85m7d/7/
Edit As requested, a variant that shows divs containing error messages instead of alert popups: http://jsfiddle.net/uwj85m7d/8/
Further reading: