**1.) You want to check first for duplicate content issues. **
*SEO MOZ has a great tool suite here that ran a full analysis of the website from multiple angles.
**2.) You want to study their link profile and anchor text. **
If they were hit hard (not due to duplicate content), then their website probably got smashed to bits by Google Penguin algorithm. This is an over-optimize-algorithm that Google used to destroy websites that had thousands of links using exact anchor matches.
*You want to use brand anchor text and mix up your anchors when link building
*Research link prospecting and anchor text diversity
*Use majestic seo or ahrefs to study your link profile and determine if the site engaged in this damaging link building tactics.
*You certainly can try to disavow links through Google Webmaster Tools, but I don't think it is a good use of time.
*Focus on high quality directories (tons of curated list online just search), free directories, press releases using the website brand name anchor text
3.) General Marketing Persona Map - Learn Who Your Target Consumers Are
Also user site bounce rates can really become a sign of website that has worthless content. I would asses the goals of the website, product, and services and start with a general marketing persona map for surfers/customers. This is huge because it will lead to a better conversation algorithm to help you build out a marketing plan to reach your target audience at each stage of their though process and decision making.
**4.) Plan your content map and **strategy
You need to setup a schedule for custom content creation, on page call to actions, and a syndication schedule to help generate social signals of engagement to your website.
Also your blog need to establish Authorship and put a face behind the content you produce.
After doing this you need to create ideas for link bait opportunities like guest posting and info-graphics if possible.
*To do all of this, I suggest getting organized and setup a team of people within your organization to help you with each stage of the project.
This will keep you busy for a while! Hope this helps. Don't be afraid to Google the concepts I mentioned if you don't understand. This is how I learned back in 2004!