The Park/Neutral switch (if you have an A/T) is in the center console below the transmission control lever. If you have a M/T, there's also a clutch switch. The Park/Neutral Switch is kind of a pain to get to. Since you're asking about this and also considering replacing the starter, I guess you haven't done any troubleshooting yet. The Haynes book's schematics are useless for the sedan - it's not covered except in areas where it's identical to the convertible or the coup. The Start Relay connections are different, as are the wire colors.
You said "The car starts when it wants to" - Mine went for months with the intermittent problem of delaying for several seconds with key in Start before the starter would run. Jiggling the transmission control lever had no effect. Finally (and fortunately at my home), it failed to start at all. Typically, if the starter is bad you'll still hear the solenoid clunking. If you don't, the solenoid could be blown but check the following first.
I must preface the following with my assumption that you have the sedan model, automatic transmission, a 4 cylinder engine and no anti-theft system.
Since the only service information I had was in the Haynes book, I had to trace this out by hand. There was no continuity from the starter relay coil to ground, which according to the Haynes schematics would have implicated the park/neutral switch. In my case, however, the park/neutral switch was fine. Contrary to the schematic, the relay coil isn't even connected to that switch. I found that if the battery is connected, the transmission is in Park or Neutral and the ignition switch is in Run or Start, there is continuity - apparently through an electronic switch somewhere like maybe in the PCM or the EATX.
First check Fuse #8 in the Power Distribution center.
Next, check the Starter Relay by swapping it with one of its identical neighbors. The Starter relay is the middle one in the group of 3 in the bottom row in the Power Distribution Center. The relays are shown in the Fuses section of the Owner's Manual.
If swapping relays doesn't fix the starter problem, try this: With the relay unplugged and key in Run, jump the relay contact terminals in the relay socket. The contact terminals are the larger ones in the middle, one above the other. Just short them together (NOT to ground!) with a piece of wire. If the starter runs and cranks the engine, then the starter's OK. This was my workaround for starting the car until I fixed it.
The relay coil terminals are the left and right terminals in the bottom row of the relay socket. Viewed from the front, the left one goes to the ignition switch and the right one goes to ground via either the Park/Neutral switch (for Coupe and Convertible) or some other path (for Sedan). Use a small bulb (NOT a brake light - too much current could damage an electronic switch. The relay coil only draws about 1/4 watt.) or a voltmeter (not a digital voltmeter - you need a meter that draws some current so it won't be fooled by a high resistance connection through dirty contacts). Check for voltage from the left coil terminal to ground with the key in Start, and for continuity to Ground at the right coil terminal with key in Run and transmission in Park. Measure from Battery + to the right coil terminal for this.
No voltage at the left coil terminal with key in Start implicates the ignition switch (that was my problem). No ground at the right coil terminal with key in Run or Start and transmission in Park implicates the Park/Neutral switch (or for the sedan, either that switch or something else, possibly the PCM). You'd have to check for this at the PCM or EATX terminals, something I haven't had to do and can't advise on.
There's also the ASD (auto-shutdown) relay - I don't know whether it affects the starter. It kills the ignition, fuel pump and fuel injectors when the PCM decides the engine has to be shut down. It's the second one in the top group of 4 in the Power Distribution Center. You can check just the relay itself by swapping it with one of its identical neighbors.