One problem related to transmission not go into gear has been reported for the 2004 Honda Civic. The most recently reported issues are listed below. Please also check out the statistics and reliability analysis of the 2004 Honda Civic based on all problems reported for the 2004 Civic.
I had a crack through my transmission gear from the inside diameter all of the way out and 75% fractured from one side of that cog cylinder to the other. I replaced part # 23451-pdm-a00 and 23531-p24-j00 at a cost of $2241. 75 at the shop and another $261. 93 in car rental fees. The failure was first checked in at the shop on 9/14/2010 at 60,715 miles but it was cracked and making the noise since approximately 55,000 miles. Shop manager told me he had not seen a gear crack like mine had in 15 years and especially at 60,000 miles and that there was no question it had been a manufactures defect.