If you rip the disk using Mac the Ripper, you should get a VIDEO_TS folder that is an exact copy of the one on the original disk, including all menus, etc. If you then burn this to disk, you should get an exact replica of the complete DVD.
Assuming you haven't been tryng to work with individual title sets inside the VIDEO_TS , it sounds like either a) You've accidentally set Toast or MTR to extract the main title only (a useful feature when trying to put a movie on a single-layer disk) or b) you're burning your finished disk in Data DVD format rather than DVD Video format. That tends to produce a disk that you can play on a computer, but you can't play it on a stand-along player and it ususally won't auto-start with the menus.
The settings for all this are very clear in Toast. Yeah, there are ways to burn these disks without it, but why bother? Anyone who does much of this evetually winds up using Toast because it's such an elegant, complete solution.