iTunes on a new computer vs M4P

If I download iTunes onto a new computer, will I be able to download my old M4P (protected AAC files) without the DRM? I haven't touched iTunes in years, but I got my wife a new MP3 player for Christmas, and was hoping to get those old songs onto it without having to burn to a cd and then back to the computer or run some shady freeware program (especially since I don't actually have any burnable discs...)