Nakamichi dvd 10s- what to replace it with?

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The Nakamichi is pretty old now (it pre-dated progressive scan, for example) and you'll have plenty of options within your budget that will definitely improve the picture and sound quality, and will also play any sort of disc you throw at it.

Models that come to mind for less than $1000 include the Pioneer Elite DV-59 AVi, Denon 3910 and the Marantz DV-8400. I own the Marantz and it would certainly fit the bill, making all the improvements you are after.

The Marantz is arguably the best for audio of those three I mentioned. My 8400 is a better cd player than my old Nakamichi MB-10, which is a similar vintage to your dvd player (and was presumably a better cd player to begin with). The 8400 is discontinued now, though I believe some are still available within your budget. Otherwise, I've seen them second-hand on Audiogon for between $600-800. A new Marantz DV7600 could be another option.

Hope that helps.