The blower for my a/c and heater has stopped working. I don't think it's the blower it's self because the other day it came on and the stopped working when I turn off the car and turned it back on. Any suggestion on what it could be or what to check first.

 

Do the DTC code test and see what code comes up. If it is 12 then this might be one of the reasons. It was for me. However before doing this you might want to get hold of the DTC code 12 guide from the repair manual and then follow all the steps to rule out any other possibility.
https://honda-tech.com/forums/honda-civic-2001-2005-78/diy-how-fix-ac-power-transistor-2041582/

 

I would start by unplugging the blower motor and supplying power and ground directly to the motor to see if the motor is the problem.

If motor works, turn on the ign. switch and test the two leads in the blower plug for voltage, one of then should test at 12.5V+, [batt. voltage] and will turn on and off with the ign. switch.

If one of the leads, [probably blue/white] does have power on it when the ign, switch is on, plug it back into the blower motor and with the ign. switch on, use a jumper lead to supply a ground directly to the other lead in the plug, [probably blue/black], if blower works, replace the blower reistor. 94

 

I would recommend fcm's three step troubleshooting suggestion too!!