I purchased a new home. Construction was not quite finished, but I was allowed to go ahead and move in. Now the contractor will not come back .

Unfortunately I hear similar stories all too often.  Sometimes the contractor is stressed and/or not very concerned about building a reputation for quality work and satisfied buyers.  Sometimes the buyer is a bit "picky" and the contractor gets burned out on repeated calls for minor details of little substance.  By saying "construction was not quite finished", you imply the issues are not trivial in nature.  There are only two ways to resolve your problem:  One of them is by somehow getting the contractor to come out and take care of whatever is lacking.  If you simply cannot get him to do that, the other way is to go to court.  If you choose to explore that route, you should hire a good contractor with a reputation for excellence; ask him to examine your home and advise you of the cost for completing the work.  Ask him to give you a written estimate of the cost and to agree to go to court with you, if necessary to testify to his opinion that the work was left in an unsatisfactory state.   I recommend that you then have the work completed and, if the cost justifies litigation, confer with a good lawyer who has experience in trial work.  Some real estate lawyers spend little time in court and prefer to maintain an office practice.  A good real estate attorney who also is comfortable doing trial work is the best. At that point you can present your attorney with the initial contract, a written estimate of the shoddy work, and an excellent witness who can testify to the shoddy work and the actual cost of finishing.  Unless you have an unusual contract, you will not be able to recover your costs of litigation. Review your contract with the builder carefully too.  Sometimes there is a provision that "moving it" constitutes an acknowledgment that the construction is finished.  If you have that in your contract, it may well defeat your efforts. If the cost of finishing is so modest as to not justify hiring an attorney, you may wish to proceed against the contractor in Small Claims Court.  You should inquire about that if you confer with attorneys and they tell you the case does not involve enough money to justify hiring an attorney.