Question edited for clarity.
The first thing to check is the fuse to the unit. The could be a fuse block for accessories on the boat, or it could be an inline fuse to the unit itself or both.
The pull all the plugs from the rear of the unit and check for corrosion. Spray with WD40 and replace the plugs carefully and tighten the fixing screws evenly.
If that doesn't fix it, it may be the transducer, but you should still get a picture for chartplotting. There is no way to check them for correct operation, but try this
https://sportfishingbuddy.com/how-to-tell-if-transducer-is-bad/
so if all that fails, you will need to return it for repair. There are some troubleshooting ideas here. This easy fix is on the Lowrance site
*Screen goes dark?: If your display turns on, shows the blue Lowrance screen, and then goes completely dark, most likely you have accidently shut your backlight off while powering off your unit.
To resolve this problem, once the unit is powered on and the screen is dark, simply press the "Power" button a few times until the screen brightens back up. Do not hold the "Power" button down, just quickly press and release the button.
To prevent this from happening again, when powering off your display, simply press the "Power" button one time and then select "Power Off." This will save all settings and features and safely shut down your display.
https://www.lowrance.com/help-and-support/?guideTitle=Display-Problems&guideId=003-043
https://www.google.com/search?q=lowrance+HDS+12+repair
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