Thank you for using the forum. My name is ***** ***** I hope to assist you today. I am another expert on the forum, and I noted that you have been waiting for an answer for quite some time now, my apologies for the delay.
Based on what you posted, it appears you have a very good argument that the company is in breach of contract for failing to provide you with the engineering report as they agreed. This means that their breach of contract (failure to perform) entitles you to a return of the deposit (you could sue them for breach, and claim that they are liable to you for any damages - such as increased costs and delay costs - for their failure to perform these reports as agreed upon).
The fact that the contract was not signed however is not a defense - you sent in the money which is going to be construed as an agreement to the contract terms as they sent them to you.
(But again, based only as you have posted them here, it appears that you have a very good cause of action for breach against this company for their failure to perform).
Short of filing a lawsuit, you can try to mediate the dispute with them - contact your local bar association and request referrals to mediators, a third party neutral can often help you reach a mutually agreeable resolution. Use the bar association's referrals to contact a mediator or two, the mediator will then contact the other party to set up a mediation session, and you can go from there - hopefully resulting in a formal or written settlement agreement, and save yourself the time and expense of litigation.