Your website should be redesigned and updated with new content to provide new data and value to your human visitors, and to let search engines (like Google) know that your website has the most current information. Otherwise, why would Google want to send their users to an old, outdated, irrelevant site?
Landing pages are used with marketing campaigns, and can help drive highly-targeted engagement from your prospects and clients. These are also used as part of a marketing funnel that leads your interested buyer toward a win-win scenario.
Keeping your website current with the most up-to-date software and security will help prevent your website from being hacked and sending out spam. If your site has outdated software and plugins, it becomes a target for malicious intent, which could get your site, IP Address and email accounts blacklisted by major providers, including Google.