In case you're still having trouble with this, to make Parallel.js work in Internet Explorer you have to include the evalPath option, as mentioned on the website:
evalPath (optional): This is the path to the file eval.js. This is required when running in node, and required when requiring files in browser environments (to work around cross-domain restrictions for web workers in IE 10).
This also applies to IE 11.
So your code will become:
var p = new Parallel(items, {evalPath: [PATH_TO_EVAL_JS]});
Where [PATH_TO_EVAL_JS] points to eval.js.