Began recently - upon a key turn - just warning lights and silence - no starter turning. Next turn may start fine. Battery is new.
No other issues. Happened after running, never cold - but unsure about a connection. Just like - one time there is no
starter connection, next time - OK. Any ideas greatly appreciated. Thanks!

If this was an old mustang, I would say the solenoid is going bad... on a celica... Well I had trouble with loose connections on the battery. My battery was not strapped down and one of the connectors was corroded.

Good luck!

Could be something with the starter

Check your Starter or starter relay (in engine bay).
Hopes that help.

Not trying to be a wiseguy, but are you sure you're turning the key all the way? You ever know...

can some one point out wheres the starter relay?

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It's in the fuse box under the hood, front left corner of the fusebox. There's a black relay and purple relay next to each other. One is for the starter, the other is for the EFI.

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Yes and just swap the two out. They are identical in form and function even though one is purple. Swap them out and if the starter problem goes away but the EFI starts cutting out and stalling the engine you know that the relay is crap. Just move em around and see if the problem follows.

Okay. My son has been using my '96 Jeep Grand Cherokee since I bought my Celica last October. He called me yesterday to say the Jeep would start. When I came home, there was a bit of extra play when turning the ignition key. All the dash loghts came on, but the starter wouldn't engage. He told me it happened a few times before, so I took out the ignition switch assembly and pulled the lock cylinder out. There is a notch on the cylinder that fits over a bump that engages the starter. That notch had become rounded (should be square), and had opened up quite a bit. Both parts were replaced, since the shavings from the cylinder could be heard when the switch assembly was shaken, and the Jeep started right up. Worth having a look, and it's not too difficult to remove a Celica's ignition key cylinder. Jeep used Torx screws and bolts on nearly everything, and the ignition required tamper-proof Torx drivers. Like a car thief wouldn't have those.....