There isn't much in your logs to work with. If you have saved a copy of the converted video, does it play correctly from the hard drive? If you don't have a media player that can play dvd-video, try VLC. www.videolan.org
I would also suggest getting a free burning program called ImgBurn. www.imgburn.com Most of us here use this program and we are much more familiar with its log files. To use it, start the program and click Write files/folders to disc. I would set the burning speed to 8x for a first time experiment with the program. ImgBurn will not cause conflicts with other software, so it is safe to use.
If Imgburn fails to burn, click on Help within ImgBurn, then ImgBurn logs... This will show you the location of the log file so you can copy and paste it here in your thread.
We normally recommend Verbatim brand blank dvds. Get the Verbatim disks with AZO on the outside label of the cakebox. These are the good type. Don't buy Verbatim "Life Series" disks. We also recommend Taiyo Yuden dvds, either as unbranded disks bought online at shops like rima.com or you can buy them under the JVC brand.
If you want to try to use the Verbatim DVD-RW disk again, I'd use ImgBurn to do a quick format of the disk before burning it at 4x speed. You can format the disk by clicking Write files/folders to disc-->Tools-->Drive-->Erase Disc-->Quick.
Or you can just click on the little red icon in the main window of ImgBurn. I'm including a picture of that for you.