My 96 Tercel has an occasional start up problem. As I turn the key to start it, there is a momentary sound "jhing"... and then nothing happens.
The panel lights remain ON. I have to try several times before it starts.
I have had this problem 3 times over the last 2 weeks.
The engine is in good shape.
What could be the problem?

First I would check the battery. Do a wiggle test of the positive and negative cables. See if they turn easily by hand on the termanals. Are they heavily corroded?
With a volt meter, see if the voltage is around 12.5V before you start. It's very common to see loose connections.

Next, a very common problem is the Toyota starters. They just click, and then nothing. Dash lights are fine. Then click, and then nothing. And on the next try, it starts. This is caused by starter solenoid contacts inside the starter. It will need replacing for that.
Hope this helps.

Read section T in the link below:

https://www.askmehelpdesk.com/cars-trucks/faq-how-troubleshoot-repair-maintain-honda-civics-46563-3.html#post235560