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Curious problem. Obviously unrelated to the plugin as no update was released that would affect any existing installation, and looking at other C7 sites, it doesn’t seem to be a problem elsewhere.
Looking at your site, it appears the commerce7.js file is added properly but never executes. I can only assume that something updated on your site is interfering with that, but no errors are present to give us any clues. I’d go through the remaining “basic WordPress” troubleshooting steps you’ve started like disabling plugins and changing themes until you figure it out.
I did get noticeable load delays from some sort of “wpmu cdn” analytics script, so start there.