The NSX Ignition Switch gets a lot of use and like any electrical switch, it has contacts which can get dirty, pitted, and can malfunction over time causing starting problems. Fortunately, the Ignition Switch is relatively inexpensive (35130-SL0-A01 - reportedly $80 or less) and can be replaced as a DIY project. It can also be cleaned as a DIY project. The remainder of this Wiki page was extracted from the ideas recommended in this thread.
The ignition switch can be removed by unscrewing 4 Philips screws - 2 to take the lower dash piece off, and 2 on the back of the switch itself. Then, unplug it and it's out. This can be easier said than done based on your size and weight and how well you can contort yourself to fit under the dash. You may also need to experiment with different sizes of Philips screwdrivers.
One point from the manual is to insert the key (but don't turn it). Supposedly that's required to remove the switch assembly from the steering column after the 2 screws are removed. The switch harness may be taped to another harness with black tape on one end and white tape at the other end. Remove just the black tape, which will let the harness swing down. It was so easy to separate and clean the switch halves in that position that I didn't bother to completely remove the white tape and take the switch out of the car and over to my work bench.
Here are some pictures which may assist with the identification of the right connectors to unplug in order to remove the switch
Once the switch has been removed, you can now disassemble it and clean it. The switch is held together with mating barbs. Just pry them apart and you can clean the switch contacts and apply dielectric grease (very important or it will pit and need cleaning again soon) and you should be good to go for another 15 years.
Prime user: drew provided the following picture of the Ignition Switch:
A quick shot of contact cleaner may be adequate to clean it otherwise try rubbing alcohol (isopropyl alcohol) and cotton swabs. The actual cleaning can take as little as 5 minutes. However, many people have found, upon further examination, that the switch had some pitting where the contact sat in the on position, so you may need to carefully sand the pits out. One tip for cleaning only slightly dirty or worn electrical contacts - use a pencil eraser. This is especially useful on plated contacts where sandpaper might remove too much material.
For more pitted surface, various people have used fine sandpaper, a fine file (such as an ignition file), or a Dremel tool. Just remember to try to maintain the original shape & angle of the contact face. One good thing is that the moving contact is spring loaded, and will do a pretty good job of compensating for an imperfect contact face. Just be careful not to drop the plastic half while you're working on it or you'll be crawling around looking for springs and detent balls.
Again, don't forget to apply the dielectric grease or a cleaner/lubricant for electronic controls, and then re-assemble the switch and re-install in the dash. $80 saved.