There are many possibilities of why you are getting very low or no conversions. However, before looking at the landing page as the exclusive cause, I would first look at your targeting decisions, account structure, and marketing message within your AdWords campaign(s). If all of those are not well executed then you may have trouble getting conversions.
Before making changes to your landing page you may want to spend some time optimizing your AdWords campaign. Keep your budget relatively low until you have enough data to begin optimizing.
While gathering data to optimize your AdWords campaign, implement an A/B split testing tool on your website so that you can begin the process of optimizing your landing page content.
One of the first things you may want to test is a compelling headline that matches the marketing message of your ad text. Look at your competitor’s ads for the keywords that you get the most clicks from and see if you can identify the key selling points that your competitors are including in their ad text and write your own unique ads to test similar worded selling points.
Make a version of your landing page for each of the selling points you are testing in your ads using separate ad groups and landing pages so that the landing page headline message matches the main selling point of your ad text. Your audience’s behavior will guide you towards the marketing message that will convert the best for your targeted audience.
Please bare in mind that this method of optimization relies upon a properly optimized AdWords campaign, so do not skip that step. This is just a few of the hundreds of things you can do and mean as a starting tactic, but by no means a comprehensive list of optimization tactics you may need to deploy.