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2004 Toyota RAV4 vibrating and grumbling when below 30-35mph

My wife’s car just recently started acting up over the weekend. She let me know that it appears to run fine when she stays above 30-35 mph, but if she goes slower the car starts vibrating and it sounds like something’s grinding. The check engine light doesn’t come on during this time. The car has over 120K miles on it. She brought it into the dealership and they took a look and let her know that it’s either the computer or the transmission. To replace the computer it would cost approx $1400, to replace the transmission it would be $3800, but if they replaced the transmission they would have to replace the computer as well anyway. So the transmission replacement would ultimately be around $5200. Our car is no longer worth that amount. We can’t afford to buy another car, and if this were 6-10 months later it might not matter because we could probably just sell the car. I asked my wife if she could bring it to AutoZone or some place like that for a second diagnostic/estimate, but she’s afraid to drive it anywhere in its current condition.



Is it true that if the transmission’s replaced that the computer also has to be replaced. If the dealership replaces the computer, finds out that it’s not the cause, then replaces the transmission with the original computer and finds out that works fine, should we have to have the computer replaced and pay for it?



Also, some other info…
As per my wife’s statement, “When I reached city driving (below 30mph) I experienced choking or slipping gears. When I stepped on the gas, the car felt as though it was in neutral and would not go right away. If I pushed harder on the acceleration, the car would lunge forward and shudder like I was a first time stick shift user. Once I was able to get on the highway and had the speed past 30mph, there was no problem.”