Finding a happy marriage amongst your burner, write strategy, blank media and player can be a frusrating issue and comes up a lot in forums.
First off, burners have much more robust playback compatibility as opposed to standalone players, but in recent years, standalones have made pretty decent advances in overall compatibility.
Although your player is 4 yrs old, your problem may be completely resolved with a change in blank media. I have a 3-4 year old samsung and it will play all my bkups. For the most part, these are Verbatim and Taiyo Yuden media. I also have some old Ridata +R, +RW which also play ok.
This would be my first suggestion as it's cheap and easy.
If you're planning on a new player, definitely follow signals' advice and take a bkup disc with you to experiment.
Another option is to purchase a dvd standalone recorder...I have 2 Liteon 5005 standalones. I think you can get one of these or its successor for about $80 or so, maybe cheaper? These units have the same optical drive that you'd stick in your pc. These guys will play anything!. Also, when one of 'em dies, I can swap out the drive for about $30-35 instead of having to purchase a whole new unit...already have a 1693s on the shelf ready to go...
If you post back with some details, we can be more specific with our advice.
Just my usual 2 cents...
Hope this helps.