In my experience developing software, I find the most important phase is the Elaboration phase. The reason I feel it is the most important is because it is the join point between the definition of the business problem and the construction of the solution.
During the Inception phase, you baseline your vision and solution to a problem and you make the business case for building it. At the end of the Inception phase you should have support and funding from the business to move forward. Everyone involved with the project should be in agreement about what the team is trying to build. If there is any misinterpretation, especially from your funding source, you need deal with it here.
The Elaboration phase is when the technical solution is determined - not actually built. This phase is the clarification phase. There is modeling, risk analysis, prototyping and refining of the requirements. This phase is when you find out if the solution can actually be built. You leave the elaboration phase with an architecture on paper (or in a modeling tool) and something that runs just enough that can prove the system can be completed successfully.
I believe this is the point where funding really needs to kick in. During Construction and Transition, headcount is being adding in the form of developers, testers, documentation writers, test engineering, release engineering, legal, etc. You are beginning to train the trainers, the sales staff, and the consultants. If the project is not going to succeed, it is in your best interest to kill it off before you begin construction phase.