Can I download Linux Mint 14 on DVD and upgrade it from within Linux Mint 9
Ubuntu supports in-distro upgrades, Mint doesn't approve of them, but even Ubuntu would baulk at upgrading over that time span.
You have to install afresh. Sadly, you have Uefi hardware. Mac's are supposed to be good with this, they have had it for some time. Linux is anything but good with it, as a quick forum search will reveal. All you can do is to make sure you have a disk image of your present setup (clonezilla on Linux, don't know about Mac's) then just dive in and try and install Mint14 on the old Mint9 partition. I would be interested to hear how you get on. If it all fails you just restore your disk image.
Others may have different ideas, so don't rely exclusively on my opinion.
Fujitsu Lifebook AH532. Intel i5 processor, 6Gb ram, Intel HD3000 graphics, Intel Audio/wifi. Realtek RTL8111/8168B Ethernet.Lubuntu 13.10,Ubuntu12.10 (Unity), Mint16 (Cinnamon), Manjaro (Xfce).