If one day that [blog] shortcode was working and then suddenly it stopped working you need to think about what happened between the time when it was working and the time you found it had stopped working. Have added or updated any plugins, for example. Have any server settings changed? Stuff like that.
I’m sure you will understand that the theme cannot suddenly come to life and decide to stop working all on its own.
The shortcode you post will display posts that are assigned to the category whose ID number is 4. If you see no output from that shortcode it most likely means there are no posts that are assigned to the category whose ID number is 4, or that no category had that ID number.
To check the [blog] shortcode is working, remove the category ID number, like this…
[blog category=""]
Does that output any posts?
References:
http://para.llel.us/themes/mingle-wp/shortcodes/blog/