If your site is reasonably modern, editable and not painfully slow, the problem is usually the content and structure rather than the technology. That is what AIVIQ's Conversion Rescue addresses: for CAD $699 we fix the messaging, page structure and calls to action of your existing site without rebuilding it.
A rebuild is the better spend when the site cannot be edited properly, runs on a platform or theme that is very slow on phones, has no proper mobile layout, or crams every service onto one page with no room to grow. In that case, see the Vancouver website redesign page, which explains how to rebuild without losing the search traffic you already have.
Whichever you choose, keep measuring enquiries the same way so you can see whether the changes worked. Neither option can promise a particular number of enquiries, but both should remove the obvious reasons people leave.