Have you had a look at connector from transducer into fish finder is it corroded?  Is battery voltage marginal a battery typically lasts 3 - 4 years  (check across battery with finder on using multimeter) should be 12V or so under load certainly more than 11.5V (does finder display battery voltage?  Some do or it can be turned on) or can you try hooking another battery up temporarily?  Does finder have a simulated mode (check manual) - if doing in this could be a display issue, if ok could be faulty transducer - would have to try another to rule out.

Spray connector with WD40 or similar and insert/remove a few times and you will then have a good connection.  Simulation mode is for use on land - usually you turn on pressing or holding various buttons and then gives you a picture so you can play with modes etc.  If reading 12V probably battery is ok - should tolerate down to 10.5 to 11V anyway - will be listed in specifications part of manual.   I assume display plays up straight away not after a time? 

Disconnected put a ohm meter between the battery terminal and the conector pin... there should be nil resistance
If there is u may have a bad connection... then need cleaning .. not just a spray of something.
 And after cleaning go to your local marine service dept and see if they will give you a teaspoon of marine grade electrical grease for the connections
 If it is not a connection check the pins each end of the cable.. may have a break inside the cable.

 If dont have a ohm meter.. check the voltage across /on the battery terminal  s and compare at the pins at the other end of the sounder cable.. should be the same.

 Caution spraying solvents into the back of the sounder  and cable pins... apparently some ppl have had issues on some brands....again best is to clean and electrical grease.

The trouble spraying electrics with crc etc is that it doesn't remove corrosion, just sot of moves it to one side... and in car engine type application, ends up having even more dust suspended in surfaces  which then creates all sort of sparking , feed back in circuits and weird stuff... like turn on indicators and a brake light or dash light go on...

 These solvents are quick temp 'side of the road' patch fixes.. not permanent or maintenance stuff

 From your description.. age putting 2 and 2 together, not actually seeing it.. I would guess that maybe something like your screen is dieing..
 Maybe time to look at upgrading...