Can I place a cease and desist on a competing company that has taken our business concept?

You can try to seek an injunction on them, but it will be difficult unless you had them sign a non-competition agreement before disclosing the idea to them. In the absence of an agreement to not use or disclose your concept, the law tends to not protect business ideas. If there is such an agreement, however, it will be enforceable, as any contract is enforceable; you would bring a straightforward breach of contract case.

If they are using something proprietary of yours (customer information, business process information, vendor contacts, etc.), that would be different; you would have a better chance of prevailing, since the misappropriation of proprietary information can give rise to a cause of action. But if they are merely creating a business for the same niche you identified, it will be more difficult.

Given what is involved, it is well worth your while to discuss the situation in detail with an attorney with business litigation experience; bring with you all agreements, communications, and other correspondence for the lawyer's review.

At the same time, you should also discuss with the attorney suing them for their failure to honor their agreement vis-a-vis developing the web concept and delivering code; you may be able to get monetary compensation or take other action which will impact their ability to compete.