A trademark protects the brand (business name, tagline, product name, logo, etc). It identifies the source of good or service in commerce. You create a trademark right by your use of the mark in your geographic area and we always advise these days that all mark holders clear then file their mark at the USPTO (federal registration).
That said, you cannot protect a "concept." I would bet the farm here as well that the NDA you speak of would likely be unenforceable anyway because it probably seeks to cover to broadly unless it was drafted by a professional.
I suggest you consult a lawyer in private and discuss a best course of action. Most of us here, including myself, offer a free phone consult so you may want to take advantage of that. I will also link you to some general helpful info below.
The law firm of Natoli-Lapin, LLC (Home of Lantern Legal Services) offers our flat-rate legal services in the areas of business law and intellectual property to entrepreneurs, small-to-medium size businesses, independent inventors and artists across the nation and abroad. Feel free to call for a free phone consultation; your inquiries are always welcome: CONTACT: 866-871-8655 Support@LanternLegal.com DISCLAIMER: this is not intended to be specific legal advice and should not be relied upon as such. No attorney-client relationship is formed on the basis of this posting.
Ideas or concepts alone cannot be protected. Major corporations have their own R&D departments and very rarely enter into discussions with beginners or outsiders.
The above is general legal and business analysis. It is not "legal advice" but analysis, and different lawyers may analyse this matter differently, especially if there are additional facts not reflected in the question. I am not your attorney until retained by a written retainer agreement signed by both of us. I am only licensed in California. See also avvo.com terms and conditions item 9, incorporated as if it was reprinted here.
Big companies often refuse to sign NDAs because they don't want the hassle of considering and rejecting a proposed project, only to go forward with something simlilar in the future. Ideas are not the subject of copyright, only the expression of them. Trademark law won't protect you. Unless your concept is sometning that can be patented, there is little you can do to.