You won't like this answer, but I'm writing it anyhow: Buy a new one.
Specifically, buy a separate VCR, and build a Mini-ITX DVR with a DVD-RW or DVD-ROM drive. It won't be cheap, but it will do a lot more for you than a regular DVD player. I'm not saying its impossible, but I have yet to see a DVD-ROM/RW PC drive fail, while the DVD drives in DVD players seem to fail if you look at them funny. If that won't work, then buy a separate player and VCR; do some research, but generally if the player costs more than $50.00, it will likely last longer (though I still doubt longer than a PC drive)...