1996 Honda Accord Do I really need a new transmission?

I have a Honda Accord that has no mechanical problems but one day were driving down the road and it went into neutral. We got it off the road and could not get it to drive again. However, if you shut the car off for a minute it will drive again for a short time. I took it to a transmission shop and they are saying i need a new transmission. Although I have talked to several other people and they say if a transmission is out then it won't drive at all. This is not the case with this car. You can drive for a short period and when it goes into neutral shut it off for a minute. Then it will drive again for a short period. When it is neutral nothing works for example reverse, or 1st or 2nd gear.