Sounds like its in neutral when in drive - 2001 Honda Civic

Sounds like the physical movement of the linkage is pulling or rubbing the harness. Get up under the dash and see how the harness is located.

Rear differential.
Going straight or turning?

clutch need to change

probaly a broken rear/lower planetary set or ring gear is broke

Sounds like a cable to the transmission is not adjusted up right, and/or the neutral safety switch is not adjusted right, if this applies to your Toyota Corolla.

If this is the only problem you notice, it sounds like universal joint going bad in the drive line. Put the gear selector in Drive from neutral and then back to neutral and then select reverse. Listen for the clunk when changing from drive to neutral and neutral to reverse. A bad universal joint will make a clunking sound when the drive line reverses direction because of the slop in the joint due to the bad needle bearings.

Sounds like the gear linkage cable needs adjusting Simple job really

sounds like your trans linkage needs adjusting.

have the transmission rebuilt sounds as if drive gears are wore out.