The vested equity clearly has value to both you and to them. You should not return it without compensation commensurate to that value. If they were serious about starting a new company, they would have done that already. They likely have not and (maybe) will not for several reasons. First, there's a lot of distraction and expense of going through that process (if they flush their idea again, do they start a new company again?). Second, there may be legal reasons they cannot start a new company: if they leave the old company, does that make you, as a shareholder, able to sue them via a non-compete clause or have other actions for remediation available to you?
As others have stated, given that you and they believe there is value in the equity you own and have earned, get an attorney on your side and find out what your options are to preserve that value. At a bare minimum, if the equity you have vested is considered so valuable to them that they are prepared to follow through with their threats of ditching the old company and starting a new one, that course of action has an $X,000 cost to them in legal, accouting, and opportunity costs. Therefore, it's in their best interest to offer you up to $X,000 to part with the equity you own.