2005 Toyota Matrix sporadic starting issue

2005 Toyota Matrix. I know, bad year. Occasionally, I turn the keys in the ignition and I can hear the starter initiating, but the engine doesn’t turn over. It’s a seldom occurance, sometimes lasting 5 minutes, sometimes 30, usually 2-3 times a week(car driven 4-5 times daily). Usually best practice for me is to walk away from the car for a time and come back later to try it. Shorter trips and rainy months tend to increase the problem. Took to Toyota dealer: replaced EMU(three times), oxygen sensor and fuel pump. None of which made any impact on problem. Dealership as never actually SEEN the problem, despite holding it for an entire week. Where should I have them poke around next?

Your problem is unclear.

When you say the engine doesn’t turn over do you mean that the engine cranks but doesn’t start or do you mean that you can hear the starter spinning but it doesn’t engage and turn the engine?

If the latter it may be the starter going bad, if the former you would probably need to have it happen at the shop so they can test for spark and fuel when the problem is actually happening.

Is what you hear a “click” sound? How many miles are on the car?

Toyotas of that vintage have a common problem wherein the starter will occasionally click but not cause the starter motor to turn. The reason for this is fried contacts.

The way the system works is that when you turn the key a solenoid activates that engages the starter motor gear with the flywheel ring gear and also engages two contact points to “enable” the starter motor circuit. Those contact points carry full voltage directly from the battery and get fried over time. When that happens, the solenoid engages the starter motor gear, but carbon and erosion of the contacts prevents the motor circuit from engaging.

Some here have successfully reworked the contacts, but the usual solution is to change the starter assembly.

Actually, on some Toyotas the dealer can order just the contacts and replace them. Total cost? About 80 bucks when I had mine done. It saved me the cost of a $550 starter.