BFK2,
The only difference between a PC's DVD-ROM and a standalone DVD player is the PC is software based for reading the disc's encryption, the .ifo files (these are the info files that direct the player, like bookmarks) and .bup (backup files), where the standalone player is generally hardware based. There are some very inexpensive DVD players that are nothing more than cheap DVD-ROMS housed in a shell.

Does any other of your DVDs skip or behave poorly on your standalone player? If yes, then I would say that the player's laser is on the way out or the lense might be dirty. Try cleaning the lense. Your PC's DVD-ROM probably has a hardier laser that is more tolerant of tracking problems or has less wear on it than your standalone player.

Considering the fact that you have already "resurfaced" the DVD, whatever that means, I would first have your friend make a copy of it using a DVD-R, not a +R. -R media seems to have a better compatability with players, especially older players.