You can buy a new starter or try overhauling the starter itself. You may have a gummed up/sticky starter. Since you are mechanically inclined, then all you have to do is to put some alignment marks prior to dis-assembly so you know how to put them back together. Only a few screws are involved.
The front side is purely mechanical (cogged wheel and planetary gears) which needs cleaning (using engine degreaser/brake parts cleaner). After thorough cleaning, use white lithium grease to lubricate these parts. The rear end is where the starter solenoid, starter motor rotor and stator are located. You need to apply a liberal amount of contact cleaner on the rotor and stator to remove the dirt around them.
After reassembly, you can test the starter operation. provided you have some jumper wires/test clips. Make sure the starter is secured since it will move during testing. To test the starter solenoid, connect the battery (+) side to the single wire connector of the starter and battery (-) to the starter frame. The cogged wheel should extend. Repeat this test several times to verify starter solenoid and plunger operation. To test the entire starter operation, you need a 3rd jumper wire in addition to the other 2 test wires. Connect the 3rd test cable to the battery (+) and the other end to the starter solenoid terminal (where the battery is normally connected). Again ensure the starter is secured as during this test, it will definitely 'jump' if not secured. With all 3 wires connected, the starter motor should extend and turn.
I have 2 I30s (similar to 4th Gen Maxima) and in both cases of starting problems, the starter only needs cleaning and lubrication.
Here is the link to Maxima/I30/I35 FAQ. You can learn a lot of information about maintenance and repair of you car from those articles.
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