Why is key sign flashing on dash when engine is on 2001 honda civic ex

All sorts of answers here, bad battery / immobiliser / keys need programming / caused by towing.
https://mechanics.stackexchange.com/questions/5847/2006-honda-civic-ex-green-key-light-on-dash

This;
The flashing green key is your immobilizer indicator. My recommendation (I am a certified honda tech) is take it to your local acura dealer and have them do a hard reset of the immobilizer and reprogram your keys.

It could also be a bad immobilizer itself. If it is a bad immobilizer, the tech will be able to tell through the diagnostic system used to program keys.

from here (Acura)
https://acurazine.com/forums/second-generation-tl-1999-2003-98/green-light-key-symbol-101-what-does-actually-indicate-889241/

https://www.google.com/search?q=Car+shows+a+green+key+after+being+towed

and finally, the Inertia Switch location via images.

https://www.google.com/search?q=2006+honda+accord+inertia+switch+location&rlz=1C1QJDB_enCA643CA644&sxsrf=AOaemvIcF8p3lOq9heeAQbjuKX_9uICdRg:1638382317504&tbm=isch&source=iu&ictx=1&fir=btzD-s8B7iONBM%252C2QPcrMisYRKtEM%252C_%253BarwIxgB4Tm8tbM%252C9kwNAGUIsp0t2M%252C_%253BGYozu8k0X6W9oM%252Ck5rcK4gXaXKv1M%252C_%253BwAk_bQK5Y0-fkM%252CeINzwLT8_AtCtM%252C_%253BweYa3hVIHdvSqM%252CLZP845vZnOjXQM%252C_%253BhNPZRRdaboslRM%252C_htgq15-SPiJNM%252C_%253B5bM89U49bFr6IM%252CUSHGYmtKfr2DtM%252C_%253BitKWxq0TsBEAFM%252C07TkLR9x1o3_ZM%252C_%253BvP77y33kyAjz2M%252CosnWW2WLJlA2SM%252C_%253BmxuW-LrEATq3HM%252CwJUh8cDQUVRx4M%252C_&vet=1&usg=AI4_-kQE4OPfUPgFL3ltoutNCUVi376t8A&sa=X&ved=2ahUKEwjPx6ngmcP0AhUBB50JHZmUBMwQ9QF6BAgEEAE#imgrc=btzD-s8B7iONBM

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I don't think your radio has anything to do with them not working, check you fuses.

Look in your owners manual at dash symbols

Sounds like the ign switch.. not the part the key goes in but the electrical switch that the key acrivates under the key part/.

Have you tired shifting it in and out of park repeatedly to free the key?

Is your Civic air-conditioned (have two fans: radiator(on the left, facing the car) and condenser (on the right, facing the car)?
Does your radiator fan run at all, when the car gets hot?
Have you checked your radiator fan relay in your underhood fuse box (far upper left, facing the car, locations on cover)?
Have you investigated the thermostat?

Leave a comment in answer and I will try to help you

I don't Believe that remote start can only be re-programed by the dealer as it is anti theft prevention device get a 2nd opinion or call the dealership ..unless something has become truly wrong with your ignition system but a remote device works without a key ...you could try to disconnect the negative terminal on the battery itself to see if it will reset itself foe a few minutes then reattach and secure it but ,,,remote works without the key yntil you wish to drive it at which point you need to insert the key to forwards position to drive it

Clean out your glove box.

Use a flashlight and look for a 5 digits sticker one the left side of the glove box (CLOSER to the radio) or under the truck.

Enter the code with KEY ON (not starting engine) position.

Write this number down on the owner's manual for future reference.

change the coil pack

yes. 2001 to 2005 is the same body.