Script Editor Web Part (SharePoint 2013)

Troubleshooting

1. Open your page and go to the browsers developer tools.
2. Check if your jQuery file is loaded or not.

Possible solutions

1. Add jquery file in Site assets library in your site and refer it in your code(You can can also use CDN. But keeping jquery file in your site is best way in my point of view).

2. If you are loading jQuery file multiple times on your page then there maybe the error because of jquery conflict. To avoid that use code given in my answer: jQuery and jQuery multi file upload scripts are not loading

Add the following JavaScript into script editor web part to check if it works.

<script src="https://code.jquery.com/jquery-1.12.4.min.js" type="text/javascript"></script>
<script type="text/javascript">
$(function(){
    alert("Test");
});
</script>

If you can't access the external web in the server, we can download the jQuery library and upload the js file into Site Assets library, then using the code below to test.

<script src="http://sp2013/SiteAssets/jquery-1.12.4.min.js" type="text/javascript"></script>
<script type="text/javascript">
$(function(){
    alert("Test");
});
</script>