The classic measures of success for a project are: time, cost and meeting requirements. These measures can be said to measure the delivery effectiveness of the project. The big missing success criteria here is happy customer! Projects can be on time and budgert, but have unhappy customers. That's a fail. Projects can be over time and cost but have delighted customers. That's a successful project!
The true measure of success for any project is a happy customer. Happiness is often proportional to the value-add achieved over the life time of the project's end product(s) of the project less its delivery and ongoing support costs.
The delivery effectiveness measures the delivery cost but does not address the value-add. So who is responsible for the ultimate value-add? The project sponsor. If your project sponsor (or their role) isn't responsible for the value-add you have the wrong sponsor and the project should be put on hold until the correct sponsor can be freed up and brought up to speed.
The most popular game in project management is to get the wrong thing right. Having the wrong project sponsor almost guarantees getting the wrong thing right.
For a more detailed view on why projects fail see Rob Thomsett's great article on Causes, patterns and symptoms of project failure.