I have a 98 Elantra. For over a year I have been having problems with the transmission when at low gears. 1st and 2nd usually. There would be a delay when switching from 1st to 2nd gear. The engine would rev up and take a long time to fully engage the 2nd gear. Sometimes it would jump from 2nd to 1st jerking the car. However at higher speed there is no problem. It was also intermittent. The day I took it for a diagnostic check at the dealer the problem went away and dealer says there was nothing wrong. He then suspected a leak and advised me to change something for over $200 which I declined. There was no evidence of any leak and I did check the Trans oil about a month back. I also changed the transmission oil 6months back to try to fix this problem.
Now about a week ago it suddenly became worst especially after the car has been parked for a long time. I then had to warm up the engine before driving.
Then one day my battery died. Really died. Dead as a rock. Could not even charge up. So I had the battery changed and guess what ? The transmission problem suddenly went away. I have been driving for the past 4 days and transmission is still fine. I do not believe it.
So next time you have a transmission problem with the Elantra do not ask why. Just change the battery !!!!