I came across an interesting article at Fast Company.  Dan Heath, the author, advises how to approach your boss when you’re certain your company’s Web site needs replacing!

In my opinion, the ultimate purpose in having a Web site is so your customers can find you.  I don’t know very many people who still go to the yellow pages to find out about a business when a Google search will generally elicit much more information.   This is the key.   The message your Web site is sending can make or break that customer relationship.   There have been times that I have gone to the internet to find a specific business, not found it, and ended up going somewhere else.  So, having a Web site is the first step.  If you think yours isn’t up to the task, then you should put your site through a few usability tests to make sure your customers are finding you and want to do business with you.   

An easy usability test is as simple as finding a handful of people that your business targets, and having them play around on your site for a while before answering a few questions.   These are the specific questions that Dan Heath covers in his article:
•    What does [our company] do?
•    Who do we serve?
•    What makes us different from [the giant in your space]?
•    Talk me through what you picture us doing.

Beyond that, it’s up to you to convince your boss!