ReadyNas died--can I easily get my data with a new NAS?

Most likely the power supply died.  IMHO, it is no longer cost effective to fix an NV+ because the protocols needed to access it are being depreciated.

No, you cannot just put the drives in a different type of NAS (not even a later model readyNAS) and have access to the files.  Depending on how the manufacturer handles it (I'm not familiar with any NAS other than ReadyNAS), it might even re-format the drives.

A Netgear OS6 based NAS will allow you to use a special procedure to recover the data form the drives, but you have to coipy it to something else and then re-format the drives for the new file format.  If you have a way to connect them all to a PC, then RStudio for Windows can also read them (https://www.r-studio.com/free-linux-recovery/ )

Yet another option is an adapter cable to allow you to temporarily attach a standard ATX supply to the NAS and recover that way.  The connector inside looks like a standard 20-pin ATX, but the pin-out is modified.  So, you need the adapter, which isn't too hard to make.  The pin-out is here: ReadyNAS_PSU_pinout.pdf .

Note that you should use masking tape or something to seal the gap where the power cable goes into the NAS so as to have proper air flow if you are going to run it long enough to recover your data.  If you are just checking that it's the power supply, a short time without it is usually OK.