I had just recently bought a new dvdr. At first I could burn music but was having trouble backing up dvds. Now it is the complete opposite. I have burned a few cds since, and they do not play in my truck but play on other cd players, and in my friends cars. I thought that the truck cd player was going out, but I burned a cd at my friends house, and it plays just fine in my truck. I have no clue.
By new "dvdr" I assume you mean a drive that can record and play both DVD-/+Rs and CD-Rs. The symptoms you describe indicate that the truck audio player is finicky about what it will play and what it will not play. That is typical of car stereo players. The CD-R your friend recorded may be able to play because it: 1) is a different brand of disc; 2) was recorded on a different drive; 3) was recorded at a different speed; 4) was recorded with different recording software. Any one of these factors or any combination of them may indicate why your disc won't play while his or hers will. Your best chance of success is to try a different CD-R disc from a different brand in the hope that it is from a different factory. Different factories use their own stampers, and it is usually an issue of groove geometry in the CD-R disc that will prevent finicky players from reading CD-R discs.