Engine Cooling System problems of the 2002 Dodge Neon

My engine light turned on initially. I took the car to a mechanic to have the computer read by a mechanic. The light turned off before I arrived to the shop, but I thought that there would be something in the computer history. The mechanic still put this on the computer which read nothing in the history. I thought that this must be some type of diagnostic check and the mechanic stated that I could of just put the gas cap on wrong or something. I just bought the car about 6 months ago and nothing was wrong with the car when I had this inspected. The engine light being on will not pass emissions. Then on 06/22/09 I got an full oil change and all fluids were checked. Still nothing wrong. I turned the car on 07/04/09 the brake light was flashing and the speedometer gauge and fuel gauge was shaking. The battery died. I replaced the battery and the battery warehouse checked the flow of the battery and stated that this may have been just a bad battery because nothing else is wrong. They even stated that this was not the alternator. Then 2 days later I turn the car on and the transmission fluid and antifreeze were pouring on the ground. I turned the car off immediately. The Dodge dealership thinks this is the transmission from experience without even looking at the car. I feel that this is a safety hazard and would like this to be looked into further when looking online it looks as if I am not the only owner of 2002 Neon that is having this particular issue without any noticeable warning. There was no pop-the engine still runs without a noise I just noticed that I lost all gears and fluids are dumping very quickly from my car. I immediately shut this down. Dodge is quoting just for a transmission the bill will be $3500. 00 and needed my VIN # just to tell that without seeing my car. Luckily my employer is not upset about the fluids all dumped in the parking lot, but this could be considered property damage.