Moving from Access to Oracle is a large change for most organizations.
* Access only runs on Windows. Oracle runs on Windows, Linux, UNIX, AS/400, VMS. Operating system selection will affect total cost of ownership. If you have no in-house UNIX help then consider running Oracle on Windows. I find it to be easier to administer on UNIX systems, but for the novice org, Windows is a more economical choice that takes OS administration out of the equation.
* Access only has one "licensing level" it is what it is and you get all the features when you install it. Oracle licensing (and pricing) is more complex : Standard1, Standard, Enterprise. You can always upgrade, so start as cheap as possible to lessen sticker shock (but present everything & make a recommendation). Each level of Oracle provides additional/optional features and scalability.
* Access does not support concurrent use by multiple users and data storage is limited to 64K rows/table. Oracle supports massive amounts of user connections, hundreds of columns & billions or records.
* Backing up and Access database ? Oracle allows backups to be done offline or online (database closed or database open and available to users; allowing 24x7x365 access to data)
* Scalability: once you move some data to Oracle you gain incremental value by moving MORE data to Oracle. Consolidate the information that people have in Excell spreadsheets, email, Access, etc. into Oracle. Combine it with a reporting frontend (every major company makes one) or even use Excell or Access as your reporting front-end. The organization will now be able to link and analyze data in new ways to gain a competitive edge or just improve efficiency. The costs of data management can now be reduced.
The cost of ownership of Oracle is large upfront when compared to Access, but this may be greatly outweighed by reliability, scalability, ability to consolidate and analyze data. The firm must be willing to commit to the proper administration of the system - this is where I see many companies try to cut costs and it can be done (ASP, DBA on Demand) but must be carefully thought through.
Happy to assist further, but to make the best argument, it helps to know more information such as the politics behind the questions you are trying to answers. Providing information is only 1/3 of the battle. Anticipating objections and Solving problems (sometimes ones that aren't acknowledge) are the other 5/6.
Your presentation is the remaining piece that will sell this change, if it is the right one to make!
Good Luck!