My brother Neumann has a 1998 Toyota Corolla and it starts completely fine for a stretch of 3-4 weeks, then unpredictably it will not start. When it doesn’t there is no turnover or clicking noise. I don’t hear anything. Weather doesn’t seem to affect it either way and putting it in different gears (neutral, reverse, etc.) or holding down brake/gas pedal does not help. Lights, dashboard elements and windows work, but no starting. Battery is okay. Any diagnosis?
Once connections are confirmed good, I bet it’s the contacts in the starter’s solenoid. This is a common problem with Toyota starters, once they’re 10+ years old. Happened to mine. The dealer sells replacement contacts, they’re easy to replace once you have the starter out.