Hello,
Yes, it could be that exact issue. Unfortunately, the Late 2012 iMacs are now Vintage, which means they cannot be repaired by Apple. Some third-party Apple Authorized Service Providers may be able to get the parts, but it could be very difficult. You may be able to source the power supply yourself, however the repair itself is very complex due to the adhesive strips that hold the LCD in place. In addition, other internal components could also be at fault, and can easily be damaged when repairing yourself without proper training.
I don't recommend you attempt the repair yourself...I would check with local Apple repair shops and get a quote.
Sorry I don't have better news...let us know how it goes.
C