Hello, I am new here, hope you can help answer some of my questions.

I have a 02 Accent 2 door coupe, automatic transmission, currently has about 118K miles on it. I got it second hand about one year ago which had about 108K on it. I got a couple problems recently (within the past 2 weeks):

1. The check engine light would come on after going for about 15 - 20 minutes, and then the car would be locked at one gear (I believe the transaxle was held at the 3rd gear for fail-safe), and wouldn't accelerate
2. There is clicking noise when the car is rolling (either in neutral gear or when I am not stepping on the gas nor the brake pedals), and is most audible at 15-30mph. The noise would be gone when I step on the gas and accelerate.
3. There is a steering free play of about 1 inch (or less, didn't measure that exactly, but definitely feel different when driving) to the left and right. When I was driving at high speed (>40mph) on bumpy roadway, I feel like it is almost (but actually not) out of control in keeping the car straight.

I took my car to an auto shop and have it diagnosed, and they found the following:

1. P1529 (MIL-on request signal to ECM) and P0734 (4th gear incorrect ratio) was detected. Transmission fluid is over filled and dirty. They recommended me to a transmission shop and have them do further diagnosis. The transmission shop said the transmission and differential are bad, and need replacement.
2. The noise was coming from the rear brakes. The wheel cylinders has no seals left and need replacement of the rear brake systems (wheel cylinders and drums)
3. No problem on steering slop was found.

My doubts here are:

• I am not sure if I was told the true story by the transmission shop because I feel no difference in shifting or gear changing except when the check engine light is on. Jiffy lube changed the ATF about 7 months ago and my car has been running fine since I got it 1 year ago. Would the transmission and differential be bad if my car is working normally (when check engine light is off)?

• Would the wheel cylinder cause clicking noise when rolling in neutral?
• Is certain amount of steering free play normal or ok for driving? But I certainly feel a difference now compared to before.

Do you guys think I was told the true story about my car? Or should I take my car to the Hyundai dealer for a further diagnosis (And pay $100 for that)? Or should I just get rid of my car?

Thanks!