I've got the LMS-335 (bought new in 2004) and have already had to replace the transducer. Unless you try a known good transducer, you really cannot isolate if the transducer or the electronics is the problem. Unless it's been crunched, nothing you can see will definitively indicate if the transducer is good or bad. But checking the wiring is a good place to start, since it's easy to do and doesn't cost anything. Doing a reset might help, but do you lose your waypoints when you do that? I seem to remember doing a reset on mine when I first got it, and having to re-input data. Luckily, I didn't have much in storage at that time. But if that's what you need to do to fix it, then you do what you have to do.
If you know someone who has the same unit, maybe you can borrow it and try it on your transducer? If you can get a transducer, just hang it over the side and hook it up to your unit. If it corrects your problem, then that's it. That's what I did, figuring having a spare transducer if that wasn't it isn't such a bad idea. At some point soon, I'll be buying another one to keep on hand.
My sonar was giving erratic readings some of the time. Very noisy display and a depth of 185' in Barnegat Bay. Then sometimes it worked perfectly.
Good luck
John