Website appraisal - can my old database-driven be updated to responsive HTML5?

General information for the website: Agricultural products website needs updating
Kind of development: Customization of existing website
Num. of web pages/modules: 12-plus
Description of every page/module: My old database-driven website with about six dynamic page types and three or four static pages is showing its age and I'd like to update to a responsive HTML5/CSS site similar in style to http://fwi.co.uk.
Description of requirements/features: I've looked for a hosted HTML5 solution but can't find anything with similar functionality to my existing Interspire Website Publisher CMS, so I'm wondering the current page templates can be changed to responsive HTML5 and the existing (PHP, I think) scripts retaine to pull in the dynamic content where required. I've attached the current default home page which should help in this analysis. The page header and footer can probably be included in each new page template rather than separate panels if this is easier, but ideally I'm looking for a solution that means all exisitng content remains accessible and the exisiting back-end of the site stays as it is. Only the front end changes and is brought up to date. A home-page template along the lines of: http://themeforest.net/item/news-time-magazine-blog-html-template/full_screen_preview/6330502 would be ideal.
Extra notes: Appraisal of feasibility only needed at this stage; although successful contractor will be given first refusal to quote for the upgrade work if it is thought possible.