RE: Car goes backward but does not forward
The initial gear (D, 1, 2, R, etc) is selected by the gear shifter. Make sure the shifter cable is actually moving the shift lever on the trans into Drive, etc.
The electric shift solenoids shift the trans into a higher or lower gear when driving.
If the cable and shift lever are working OK, the problem is most likely inside the trans, a clutch, brake, etc.