How do I get my company's Global IT department to work on divisional projects?
Underserved in Florida
Can I suggest a liberal sprinkling of Captain Kirk figurines?
Seriously though, this decision is probably above your pay grade. Assigning resources to projects must be done by the management team who OWNS the Project Management process at your company. My guess is that there is little PM maturity within your company and departments are being allowed to practice bad behavior like hogging their own resources.
What your company needs is a steering committee made up of Director or VP level managers who commit to running projects within the company properly. This team will prioritize the company projects by business importance and then fully staff the top projects until all the resources are used up. At that point, the remaining projects are put on hold until new resources appear, either through hiring or finishing existing projects.
When resourcing projects, the steering committee must ensure that each department frees up enough resources to man all projects: functional, global and divisional projects. If a project does not have a needed resource, it needs to be placed on hold. If many projects are fully loaded except with IT resources, a tremendous pressure forms on the IT head to free up resources to get these projects accomplished.
Until this happy day comes around, what can you do? Like any other project obstacle you come across, you need to influence the decision-makers to get the IT resource you need to accomplish your needs. Find out who has the authority to make that decision and set about influencing him/her to give you a resource. Use your sponsor, show off the project benefits in a way that is personally relevant to the stakeholder, befriend him, whine, beg, do whatever it takes to get the person you need. Threaten to hire a consultant, actually do hire one. If this is your project's biggest problem, you need to resolve it.
Meanwhile, make sure that all status reports indicate what the lack of this resource is doing to your project's schedule and cost. Elevate this information as high as you can until the problem is resolved.