Can someone please tell me why this is considered a sentence fragment and offer suggestions on how to fix it?

No no no ignore Microsoft Word, it's being an idiot. A sentence fragment is the standard form for the title of a research project. It's a label for the project, not a claim or a proposition, so it doesn't have to have a main verb, or indeed any verb at all. I've spent years and years in multiple graduate programs, and I guarantee your title is totally fine as is. In fact it sounds really interesting. |^)

Since it's your title, don't worry about it. I think the computer might be thinking you need to do something like this:

An Investigation Concerning the Legal Ramifications of Using the Internet as a Means for Determining Employment Eligibility was held last thursday....blah blah blah

does that make sense? forget all the capital letters and it might make more sense, but it probably thinks you are introducing when or where "an investigation" was held

but don't worry about it. and good title, it gives a clear idea of what you will be discussing

It's a sentence fragment because there's no verb that corresponds with the noun "investigation," but I can't see why there would be anything wrong with your title being a sentence fragment.

Unless your teacher said otherwise, most titles are absolutely fine being fragments. They aren't expected to be sentences.