I have a 1994 accord. When you have gone about a mile or so, the transmission will not shift into 3rd gear. It is an automatic. I have had numerous suggestions, but most were far fetched in my opinion. Do I need to just scrap it and cut my loss?

Most likely, you are looking at a rebuild situation, particularly if the transmission fluid has not been changed regularly and the car has a lot of mileage on it.