Do you need a blog for your business to do well with SEO? The answer is no, you don't NEED a blog. But, that doesn't mean you don't need to have lots of good content on your website. Whether in the form of a blog, or in the form of pages, content is KING! And by content, I mean original content that is posted frequently.
I have found that individual pages actually often do better with SEO than blog posts, so if you don't want to have a blog on your website, instead build a section of your website where you build lots of pages with lots of well written information that can be a resource to users. For example, see my www.picklewix.com/wix-tips section on my website design site, I have created tons of pages on different topics about Wix Tips. So for your business, you could create a section about FAQs about your services or products, and then create pages on a regular basis with new written content with information, answers and tips for your users. As users find these info-packed pages, they will start linking to them for more information, which helps build legitimate inbound links. You can even use Google AdWord's keyword planner tool to do searches to see what people are searching about regarding your services or products, and then write new pages with the searched individual keyword phrases as your focus point.
So, no, you don't NEED a blog, but you do need content! So whatever form you choose to use, just make sure you write original informative copy, and original images (with alt tags!) and create new content often!