you could just copy the files from the DVD's onto your hard-drive, you will have 2 folders: AUDIO_TS and VIDEO_TS, navigate to the VIDEO_TS folder and copy the files with the ".vob" extension.
If you just want to chop out chunks with no editing the easiest way would probably be to re-name the .vob files to .mpg, this will allow you to import them into your DVD authoring application, if you have one, if not, download a trial of one,
import the re-named vob's in the order you want and create a menu as normal with the files, they will be DVD compliant already so you shouldn't need to transcode, then burn the new DVD.
if you need to edit/combine the vobs you may be better off using something like VirtualDub mod to convert the vobs to AVI's and editing before transcoding to MPEG2 for the DVD.
This is probably a badly written explanation of what to do, if you can't follow it, or if you post some more info on what software you use/have on your PC I (or someone else) could give you a better version. But it is definitely possible to do with what you have.
Hope that helps
Panasonic SD9, Panasonic NVGS-75, Canon MV600i