ReadNAS Pro 6 stuck on 'ReadyNAS' when booting

There are actually a multitude of things that can cause that, as the "ReadyNAS" message is stored in the display and the NAS just needs +5V (and not very well regulated +5V) to display that.  But StephenB​ is correct that the power supply is the most common.   I've bought (and then repaired and resold) several with that symptom, and only one in the 6 I bought had something wrong other than the PSU. 

The 6-bay legacy units (Pro and Ultra 6 models)  actually have a standard pin-out and a standard ATX supply can be used externally with no pin-out modification.   If you have one available (even if you need to temporarily "borrow" it from a working PC), you can quickly find if that's the issue doing that.  If you use an external supply for a long period (if you just want to get your files and then plan to ditch the NAS, for example), then make sure you take precautions to insure the fan moves enough air over the drives.  Cover the PSU fan hole and any gaps where the cable comes out with masking tape.

A standard SFX supply will work as an internal replacement, but most need a 24-pin extension and more 4-pin  MOLEX connectors.  While the original is 250W, it has more +12V wattage than most 250W, so I recommend at least a 350W one.

While it used to be a bit cheaper to buy a standard supply and add those features to it, there is a pre-modified one available on eBay that now has a price that's about what it would cost to do it yourself and is a whole lot easier.

If it's not the power supply, there isn't a lot more that's user serviceable.  RAM and the CPU are it.  A bad CPU is rare, but bad RAM is a possibility.