JVC DRM10 disc error, can't format disc
 

I have several DVD-RW discs that were used in my Magnavox DVD recorder.
I want to use them on the JVC.
These discs are now empty, but the JVC won't format them.

EDIT:
I got a brand new DVD-RW disc (Fuji made in Singapore, great discs) and the same error.
The JVC thinks that there isn't a recordable disc.

Are these 2x DVD-RW or 4x DVD-RW? And then verify that these are DVD-RW, not DVD+RW.

If it's confirmed to be a 2x DVD-RW, then try a full format on the computer, using ImgBurn.
Sometimes burners/recorders do a "dirty" write, which requires a full blanking in a computer before working again.

But it does the same thing with a virgin 2x DVD-RW disc (Fuji made in Singapore, a brand that worked flawlessly before). I still had a box of 5.

Well, if you've managed to considered every possible options that is disc-based, then the drive may finally be going out. After all, it's an 7- or 8-year-old unit. That's assuming it's one of the LSI Logic models, like the DR-M10S or DR-M100S. I don't recall which model you have. It can be repaired, with the right parts.

DVD-RW are the hardest of all media to read/write, and first to go when the laser is weakening.

But I'm still not convinced it's definitely NOT the media. ;)

I have the DR-M10.

I also put in a regular movie DVD and it got the same DISC ERROR.

I suspect the drive needs to be replaced.
Where can I buy a replacement drive?

It depends on which model is inside the unit. Open it and look. You'll need to swap it with an exact or near-exact copy of the burner. You can gut another JVC recorder, or find a computer burner. Remember that DVD recorders are just using normal DVD burners most of the time -- it's not a special recorder. At most, they're using a specialty wire for data transfer, which can be modded.

I've not yet had to repair a JVC recorder's drive myself, but have advised many on how to do it -- successfully, too.

You're pretty much stuck with buying from eBay. I don't think JVC has parts available anymore (but feel free to check).