There's an infinite number of reasons why people may not be buying and frankly there's nothing more important than answering this question, yet it's the hardest to answer.
Doing more SEO or Advertising won't changes things... if reasonably qualified visitors are bailing the issue is deeper.
Unfortunately it's the hardest question to answer. I try to break it down into a few areas and map them out before doing any work:
the market - who is the customer, what are they buying, what are the other options
the message - what are you offering, what makes it stand out
the delivery - how do you spread the message, to whom
Think both broad and narrow. Sometimes issues are as simple as a headline, other times you realize you have an audience but it's a bunch of people in CA while you are in NY, and every now and then it's just a fundamental shift like your pricing structure.
Your client has tasked you with driving business under the guise of web marketing but it's not about the web, it's about discovering what will motivate people to pick his or her business over another option or even no option.
I have suggested using Groupon or Facebook advertising
Don't take this the wrong way but you're throwing mud at a wall and hoping it sticks. That's a very painful way to find success.
Take groupon, a service that is about getting new customers in at insane deals to sell to them over time. Unless I'm missing something, your client's business is really about a one time or at least once in a reasonable time period sale... The two do not work together.
Facebook works very differently as a display media source but if you can't find success in an intent driven user, how does paying for one in an interest driven market change the equation?