To answer the subject question, generally the Michigan statute of limitations for a breach of contract claim is 6 years. However, there are other period lengths based on the type of contract.
The question regarding suit depends on whether there is a written contract and what the contract says (i.e., did it specify a time period by which the work must be completed).
I would recommend talking to an attorney to properly review the document (if there is one) and the situation. If you are unable to find a local attorney with whom you are comfortable, feel free to contact me.