How much effort and money should I invest in a existing landing page?

What you've learned is that if there is anyone willing to buy your product, they are not searching for it with Google using the Adwords you chose and those that found your site didn't give you any indication they would buy your product (Click on some button for fill out a form, etc.). Figure out how to drive the right people to your site, then you can test what will make them buy.

Tough to give specific advice, but there are a few things you need to consider. Identify the market: those that will go online and buy your product. It doesn't matter if you have a great product that people like and would even pay for if they are not going to shop for it online. You could be dealing with a market that needs more hand-holding and wants a live person to answer a bunch of questions and walk them through the entire installation and testing process. All of these things are just obstacles to deal with, but until you identify a market, you can't figure out how to sell them your product.

Susan does have the right idea that you need to talk to anyone close by about what you are considering. They have to be someone in this market. If you have an iPhone app idea for Limo drivers, you better go find the nearest company and talk to them about it: do you carry smart phones, do you buy apps for it, would your company buy you one if it did this, that and the other? Most will cut you off and say, "You know what I really need..." Also, find out how this market gets its information. Find the publications, websites, user groups, organizations or conventions that are popular. Try and present your site through these channels.

Zuly has a point about people not being able to understand some products until they see a working model. The more original your idea or the less knowledgable you market is about technology will determine how much you would need. That doesn't mean if you build it they will come.

Find some way to have conversations with real people to validate your idea. Relying on Adwords is not feasible in my experience (even though Tim Ferris swears by it!)

The trap with putting up a landing page and running an adwords campaign is that you don't get any feedback about why people are NOT responding to your offer and you will never really know if it is your idea that sucks or just your marketing.

If you get face to face (or even on the phone) with potential customers, you will get both positive feedback and criticism and you will be more likely to pick up the nuances that make the difference between whether your idea flies or not.

Skip the landing page.

If you are relatively unknown (like most of us) the sad truth is that most people are not going to even know you are out there. So you're probably not going to get that much traffic (Adwords alone isn't going to cut it). And it's hard to get any reliable information/statistics without a big enough data set. You say you "have gotten quite a few page views", but I'd be curoius to know how much that really is. When you are first starting out, it's easy to get excited over small numbers (I've been there myself).

But let's say you are getting a lot of traffic, the next problem you are going to encounter is that because people don't recognize you, they don't trust you. If I don't know who you are, why would I risk giving you my email address and other personal information just to have a chance to try out something that may or may not be of use to me?

So the point is, that what you've seen so far is not necessarily an indicator of how good your idea is. Don't give up on your idea just yet. Take Susan's advice, and ask people in person - you'll get much better feedback this way.

Should I abandon it completely and try something different, or should I follow my gut and try and work on the landing page more, do more A/B testing and maybe invest more money in the adwords campaign?

None of the above. My advice would be to stop investing time on the landing pages and start building your MVP. See if you can spend a month or so building a very bare bones product. Then let people try it out, and get some feedback from them. I think this is where you should be focusing your energy. Most of us don't have that great of an imagination, so until we actually see something working, we may not really see the value in it.