The car will start only if the distributor is fully advanced. If I time the ignition with the light to where it is supposed to be it will not start.

The internal distributor sensors (CKP, TDC, and/or CYL) are likely bad. Install your current ICM and coil in a genuine Honda distributor housing only. If the problem persists, install a new aftermarket ICM and coil in your new distributor housing. Because of the age of the vehicle, it's preferable to install a new ICM and coil now in the housing. Be sure to apply silicone heat transfer compound to the back of the new ICM; otherwise, it won't last long.

Sorry, If any of those sensors were giving an issue, it would throw a check engine light. If the car is running only with the dizzy advanced.. then you probably are off with the timing belt on the car. You did not include the mileage of the car, or if this service was done recently. However, if the belt is old, it could stretch or the tensioner could give way and make the timing a teeth off. Double check you timing and see if its off.