Need hardware service on a ReadyNAS RNDP6000

It is completely normal that you cannot log into the NAS GUI with no drives installed because the OS runs from the drives, so it can't run with no drives.  All that is running on your unit is the boot loader.  But that it is running is a good sign that repair is possible.

I agree with StephenB  that it is possible that one drive is causing the problem.  Though possible, it's unusual for the power supply to fail in such a manner that drives will spin up but not enough to properly boot.  Two steps you can take are to test each of the drives with manufacturer's tools using a PC and to use a scratch drive in each bay to check that the SATA subsystem is OK.  When using a scratch drive, you'll have to go through the set-up to create a volume on it the first time.  Then, just power down, move the drive to the next slot, and power up to see if it still boots.  Do that with all bays.

The power supply is a standard SFX form factor one, and not really all that hard to replace.  If you have a spare ATX supply around, you can use that externally just to see if the supply is the issue.  If yu want to see if a local repair shop is willing to try and repair it, pass this information on to them.

I honestly don't think it would be worth the money to pay for shipping to and from a repair location, labor, and parts, even if one did exist and the problem did turn out to be the supply.