Transmission problem
 

I have a 2000 DX honda civic (Automatic). Recently while I am driving, for example when I stop behind the traffic light, an I push the accelerator, it doesn't operate. Even at that moment when I change the gear it still doesn't operate. Then sometimes when I turn off the car and turn it on again it start working.
I showed the car to a mechanic and he said it is transmission problem, but he doesn't know which part, and he told me it cost me 2800$ while the price of car is 2000$! So I want to try to repair it myself. Mechanic said it happens more when the car is hot.
Does anybody have a clue how I can repair it? is there any cheap part of transmission that by changing that I may solve the problem?
Thanks!
Rami