Is it the starter, or, what should I check?

I replaced the battery in my 1992 Toyota Previa (301 thousand miles).

It started fine for 2 or 3 days, now suddenly, it won’t turn over.

I checked the headlights to confirm there’s power, but I don’t know what else to check. Any suggestions?

Check the connections at the battery terminals. The lugs on the ends of the battery wires may be oxidized, they will appear dark when they should be bright. Also, check the bond between the wire and the lug for corrosion, this will appear as greenish color of the copper wire, and or white powder caked around the bond. Make sure the small wire on the positive terminal is connected.
If all that is good,you may have a starter or ignition sw. problem.

Toyota starters often behave like this when they get old, the starter solenoid contacts wear out, causing an intermittant ‘no start’ condition. If you have a cooperative mechanic he can just pull the starter and replace the contacts (side and center disc) for $50 in parts + labor, or you could just replace the starter. That’s after all the connections are checked, of course.

Check under coating of big red hot wire coming from battery.