It is definitely power supply .. if you open it up tell us if it is delta brand.. Apple did use a second brand to Flextronics.. Delta being one of the really big players in the power supply industry in China and with good quality products.. they did seem to last longer.. although they are not easy to fix.. normally when dead they are throw away.
Repair is probably not worth it but here is how to do it.
SSD is pointless..
The TC much too slow for an SSD to be of any use..
People have tried.. see the review here where they substituted SSD and got worse performance.
If you want to reduce power consumption use a 2.5" 1TB drive.. but the 3.5" green drive is much cheaper and really just as good.
Thank you for your encouragement, I have replaced the faulty power supply, installed a brand new WD green drive and improved the cooling mechanism. I didn't change the control wire though. Instead, I have placed the temperature sensor in a heat sink inside the power supply... It made the fan work more frequently and keep the power supply cooler.
Everything is documented here:
It's in Brazilian Portuguese but the pictures say it all.