It could be a lot of things, unfortunately. I doubt it's your burner. Here are some possibilities, not in any particular order.
1) Your DVD player doesn't like your media. I generally recommend people avoid cheap, no name media. Try burning to better quality CD-R discs or try a CD-RW disc and see if you have better results.
2) Your DVD player may insist that the SVCD video file be in a different place than where Nero is putting it. Some players won't play SVCD unless the video file is in the MPEGAV subdirectory instead of the normal MPEG2 subdirectory. This goes against the standards, but I do know of players that insist on MPEGAV. Nero has an option in making SVCDs to use MPEGAV instead, so try burning with that.
3) Nero does not produce truly compliant SVCDs, although they are close. They might be just off enough to cause problems with your player.
4) You might have PAL/NTSC issues. Your friends reporting that they see black and white on your discs can be a sign of this. It could be that you are burning
PAL SVCDs when your player will only play NTSC or vice-versa. It is possible to convert from PAL to NTSC or vice-versa, but I don't remember what software can do it. You might go to
http://www.vcdhelp.com and download both the PAL and NTSC SVCD samples, burn both, and see if your player has problems with one of them. If your DVD player won't play any of the samples correctly and the MPEGAV trick doesn't help, it might be simply that your player has problems or doesn't support SVCD very well. Some recent posts have talked about fooling players that don't support SVCD but do support VCD into playing SVCD by authoring the disc as a VCD and you might try that if all else fails.