It seems your ignition switch has burned out - verifying good starter operation was an important component in furthering your diagnosis effort. The ignition switch is really a relay separate from the ignition key cylinder - when it fails to send battery voltage to the starter motor, you'll have the no-start condition described.
See the Honda Ignition switch replacement illustration below.
Just for completeness' sake, here's the generic response of a mechanic to a vehicle's no-start condition:
Priority Action Part Type Cause
1 Inspect Ignition Switch - Improperly Connected or Faulty Ignition Switch.
2 Inspect Battery - Battery Discharged or Faulty.
3 Inspect Battery Cable - Coroded, Broken, Shorted or Poorly Connected Battery Cable.
4 Inspect Solenoid - Starter Solenoid Faulty.
5 Inspect Starter - Starter Motor Faulty.
6 Inspect Wireset - Worn or Damaged Spark Plug Wires.
7 Inspect Ignition Coil - Faulty Ignition Coil.
8 Inspect Distributor Cap - Loose, Cracked or Worn Distributor Cap.
9 Inspect Spark Plug - Incorrectly Gapped or Fouled Spark Plug(s).
10 Inspect Distributor Rotor - Loose, Cracked or Worn Distributor Rotor.
11 Inspect Fuel Tank - Fuel Tank Empty.
12 Inspect Carburetor - Worn, Faulty or Damaged Carburetor.
13 Inspect Fuel Pump - Faulty Fuel Pump.
14 Inspect Choke - Stuck or Improperly Functioning Choke.
15 Inspect Fuel Filter - Clogged or Dirty Fuel Filter.
16 Inspect Fuel Pump Relay - Faulty Fuel Pump Relay.
17 Inspect Fuel Injector Pressure Regulator - Faulty Fuel Injector Pressure Regulator.
18 Inspect Fuel Pump - Low Fuel Pressure.
19 Inspect Engine Control Computer - Incorrect Operating Information Being Delivered and Sent From The EEC.
20 Inspect Fuel Pump Strainer - Clogged or Dirty Fuel Pump Strainer.
Illustration courtesy honda-tech.com (from 1994 Honda Civic EX manual).
http://honda-tech.com/showthread.php?t=2577784
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