I hate to let you know this but, you probably blew your instrument cluster when you installed your cd player. There is an illumination and dimmer wire on a factory radio controlled by the headlights being turned on (illumination) and your dimmer switch on your instrument cluster. If you accidentally cross these wires or connect a 12V to I think the dimmer wire on the car ( one of the two wires) then you can blow the circuit board on your instrument cluster. I have read about many people that accidentally hook there accessory wire on their car to one of these wires and the next time they drove their car the lights and readings were all screwy on their instrument cluster.
You can do a self diagnostic on your civic instrument cluster by following these steps :
1.) Put your key in your ignition but, do not turn the key.
2.) Push the trip meter button on the instrument cluster and hold it for 5 seconds.
3.) While holding the button, turn your headlights on and wait 5 seconds.
4.) With the headlights still on and while still holding the button, turn the key to the on or II position, without starting the vehicle.
5.) With the headlights still on, release the trip meter button an within 5 seconds press the trip meter button four times.
Now you should see multiple dummy lights blinking and all of the needles sweep from min to max and back to min.
6.) After the needles have swept and returned to normal hit the trip meter button one more time and you should hear a beep and see the needles sweep again.
7.) Wait about 30 seconds to ensure an error does not appear on your odometer.
If there is no communication error you should see 888888.8 on your odometer.
Try this and let me know what happens. Good Luck.