Re: Remote box?
Try starting the motor with a remote starter switch. You can make one yourself or buy one at an auto parts store. They're not expensive. Just hook it and the battery up to the starter as per directions. Use it as if your are doing compressions tests. Remove all the spark plugs, make sure the motor is in neutral, and press the switch.
If that works then either your remote wiring is bad or it was hooked up incorrectly. There are any number of things that could keep it from working properly and they are fairly easy to service. Get a factory service manual, which is worth its weight in gold, and a multimeter. There is an entire chapter devoted to testing and servicing the remote. A word of caution is in order. Many times, a motor and remote are not original to each other. Make sure that your particular remote is the same as is in the service manual. The same remote may be used in a wide range of years and models. I know for a fact that the remote in a 1990 120hp-300hp service manual is basically the same as yours.
Hope this helps,
Bob