First, verify that the person that sent you the book is the person that was offering the deal.  If it is, wait for them to respond to you about why they didn't send the second book.  It's probably just an oversight on their part.

If the book you received is the book you ordered, then you're obligated to mark it received.  Even if you don't get the second promised book.

My first thought is that the person you actually received the book from is not the person you PM'd about the deal.  If they canceled the request, let it time out or denied RCs then it would have rolled over to someone else.  If you got off their book page somehow, the request could have gone to a different member.  This can happen if you have the little yellow book info thingy open on their bookshelf or if you order from the book description page instead of the actual bookshelf.

The best place to find deals on books is the book bazaar.

First, don't panic before hearing back from them, it could have just been an oversight or they could have mailed the free book separate (yes, some people do mail books separately). Give them a chance to fix the problem.

Deals negotiated between members are outside the the system and are on the buyer beware system. You will be required to mark the book received properly even without the deal book because that book you have was received according to site requirements.

It may be a situation of the request going to a different member. If you confirm that you got the book from the person you had made the deal with and they are not willing to honor their deal, do let the site know through Feedback via the Conact Us link below that someone is agreeing to deals to get requests and then not honoring them. They probably can't do anything about your deal, but they can have a talk with a member if they are offering false deals.

On a side, if you are requesting books through the system, hopefully you are willing to take just one book without a deal if the sender isn't offering a deal. It isn't fair to the first person in line to be requesting their book and the cancelling on them if they don't agree. If you only want books that are available in the system if they are in deals it is best to post in the Book Bazaar that you are looking for someone offering a deal on them. That way you aren't tying up the first person's book with your request if you aren't willing to take it.

Sender is claiming the deal they were offering did not appy to the books I ordered and that they did not get my PM about my "freebie" book. I don't belive them and have send feedback to the site.

I can't see your original question as you've redacted, but from what I can tell, I'm pretty sure the site can't do much. They don't administrate or guarantee deals made outside of the PBS system. Is it at all possible you accidentally didn't hit "send" when you sent your message and navigated away from the page by mistake? Obviously, if it's in your Sent folder, this isn't a possibility.