How can I capture the browser rendering time?
Loadrunner is a tool that captures at a level below the browser (for example at the http level). It isn't a browser, and thus doesn't do any rendering that could be captured.
There are tools that hook into the browser itself (such as HTTPWatch). see: http://blog.httpwatch.com/2008/05/14/using-httpwatch-to-measure-page-load-times-for-new-and-existing-users/
The available tools vary by browser. Chrome has a built-in debugger; see https://developers.google.com/chrome-developer-tools/docs/timeline. For Firefox, see https://addons.mozilla.org/en-us/firefox/addon/yslow/.
Just marketing a tool that R&D of my company (SendGrid) has developed for load testing, that you can give a try: