I can turn the ignition key to the on position but it will not crank the car

Sounds like your fuel pump relay is out. It's very common on these older Hondas. Quite pricy too.

Try start the car again when it is completely dry, if it starts the rain may be short circuiting something on the loom in the engine bay.

If it still wont start,

will it turn over? (car tries to start)
- If it wont turn over the battery would be dead

- If it turns over but wont burst into life then we can go from there ^_^

check the fuel pump relay and fuse.

Put the key on ACC. Does anti theft light up and stop? If it keep flashing while your cranking then it is the ANTI -THEFT. (by the way the humming noise ifs the fuel pump). If the anti theft doesnt light up during the cranking youll need the ignition module why I say that if it was crank position sensor the fuel pump wouldnt activate. your safe with the ignition module.and if you want it doesnt hurt to replace crank sensor why I say this the year.Its been a while just a suggestion

Here is the manual
FUEL PUMP SHUT-OFF SWITCH After a collision, if the engine cranks but does not start, the fuel pump shut-off switch may have been activated. The "Fuel Reset" indicator light will illuminate in the instrument cluster. The shut-off switch is a device intended to stop the electric fuel pump when your vehicle has been involved in a substantial jolt. 1. Turn the ignition to the OFF position. 2. Check the fuel system for leaks. 3. If no fuel leak is apparent, reset the fuel pump shut-off switch by pushing in the reset button. 4. Turn the ignition to the ON position. Pause for a few seconds and return the key to the OFF position. 5. Make a further check for leaks in the fuel system.
The fuel pump shut-off switch is located in the passenger's foot well, behind the kick panel.

If you turn the key from off to run ( do not start ) does the theft light go out ?
How did you check the fuel pump relay ? My 2001 at ~ 35K miles the fuel pump relay went out, I checked it by swapping the trailer tow adapter reverse lamp relay into the place of the fuel pump relay.
The thing I am drawing a blank on, and you seem to confirm what I think, is the fuel pump relay is removable in the '02. Must be the '03 when the fuel pump relay became integrated into the fuel panel ( non serviceable ).

If you jumper the fuel pump relay, does it turn on ( red line in picture below )

A bad crank sensor (it has 2) is probably the reason, a very common issue. Replace the lower crank sensor.

I had a similar problem with an older corvette. It was the chip & reader on the key & ignition. It would fail me at the worst times! A new key & sensor did help but it was kinda pricey for what i got. Also check to see if your fuel pump is working properly. Locate the schraeder valve on the fuel rail (looks like a tire valve), turn your ignition on but dont crank. Push the centre of the valve in & see if any fuel squirts out. if yes, ur good, if very little then ur pump is being a Btch. The security feature usually triggers the ignition, not the fuel pump... This is a simple "no tools" procedure. Using the proper analytical gadgets will give u much more info...

id remove the fuses, icm/ecm, fuel pump, etc. check the ignition switch it might be interanly stuck on the on position

Maybe a security passlock problem or ignition control module.Could still be a fuel pump issue.pump may run but not be building pressure!