Would I be right in thinking it is terminal?
Yes.. it is dead.. RIP.
However you can resurrect it.. the economics are something you will need to work out.. but I assume yours is gen2 on the bottom it will have A1302 as model number.. the issue is very clear..
You need a new power supply or to repair the existing one.
https://sites.google.com/site/lapastenague/a-deconstruction-of-routers-and-modem s/apple-time-capsule-repair
If you want an easy way.. just hunt on ebay for Time Capsule power supply
Several places on ebay are selling the old unused or refurbished supplies.
Installing a replacement power supply is not hard.
https://www.ifixit.com/Device/Apple_Time_Capsule
Is it worth it?? All depends.. how DIYer are you??
The hard disk might go tomorrow.. so if you can just use it as airport extreme (equal to gen3).. then it can be useful still.