Ready NAS NV+ (RND4425) keeps restarting

A PSU problem certainly can cause problems such as you are experiencing.  But getting a new one to find out if that's it is risky for such an old unit.    You can use a standard ATX power supply externally with an adapter cable to see if that's the problem and/or recover your data.  Although the connector on the NV+ PSU is of the same type as an ATX supply, the pin-out is slightly different.  So, you will need to get a 20-pin ATX extension cable and cut a couple of lines.  If you find the PSU is the problem see here Inexpensive power supply replacement for legacy 4-bay Readynases for an option to replace it.  You will also fnd a link to the pin-out in that thread.  Replacement supplies are also available commercially, but are frankly rather expensive for resurrecting an NV+.

While there is a path to move drives from x86 based legacy systems to x86 based current ones for data recovery, there are no options for SPARC based units.  But you should be able to transfer the data to a new NAS with Rsync.  Even if the unit restarts in the middle, the next backup session with Rsync should start where the last one left off.  So as long as it keeps being able to restart, you should eventially get to the end.  Windows archive bit backup should also work so long as all the archive bits are set to start with.  You could use that with a new NAS or a USB drive.

If you are not familiar with the Windows archive bit, its meaning is the opposite of what you might expect.  When it is set, it means the file needs to be archived, not that it has been archived.  Most Windows file operations will set it by default.