Can a DVD recorder finalize DVD-Rs written on a different unit?

How do I finalize DVD-Rs recorded on a Sansui DVD recorder when the unit is no longer functioning?
My Sansui VRDVD-2005 VCR/DVD recorder died -- when I still had dozens of DVD-Rs yet to finalize. The VCR deck locked onto a tape and went kaput. Because the DVD deck would never work without first inserting a VHS tape, pressing play and then switching over to DVD, the entire unit is essentially nonfunctioning. I'm sort of glad to be rid of this model but still need to finalize these DVD-Rs in order to watch them on another player.
Do I need to track down another Sansui or can I do this on any DVD recorder?