The first thing I'd do with these 2 files is to join them. I'd use VirtualDub (free) to do this.
Open the first, append segment - the second one - and then go to the video tab & select Direct Stream copy. Then save as "new name".
Then using any of those you've purchased , probably WinAVI being the easiest, conversion should be fairly straightforward.
The problem playing these on your DVD player could be down to your burner & the disks you're using.
So what burner & what DVDs? Use Nero's CD-DVD Speed & the disk info tab , saving an image (top right , the floppy icon) as a png file & posting that image here (Go Advanced & Manage Attachments) will tell us both.