So I had this issue for quite a few months now (September 2020) and while cleaning up my desk, knocked the jumper pin (paper clip) that’s used to keep my Synology DS1515+ running. I had to waste some time re-finding the video that lead me to this hackery – video below.
Essentially, you can use a regular power supply AND the existing faulty power supply to have the device boot up. I had to recall this again as I was about to remove the power cable connected to the Synology Diskstation but I forgot that I needed it.
Although your mileage may vary, this worked for me! Synology no longer provides spare parts for it so they were of no help and I haven’t scoured the web for the power supply unit. eBay appears to have one for around $190.
If reconnecting the pin, disconnect both power cables from the standard power supply and the Synology.
Don’t mind the mess in the photos. But this is how it’s currently setup and working. I think down the line, I’m going to just update to a newer Synology NAS because it should be able to be migratable. Hope that helps!