If the transmission isn't going into any gear, I suspect that your fluid is all leaked out. I would look at the lines from the transmission to the radiator (as you suspect.)
If you get that resolved and the transmission is still giving you problems, then you may need to investigate the more expensive option. It basically depends on how long you ran it dry. If you were able to successfully put it in park when you pulled over, you may be ok.
As far as having the lines replaced, if they did not tighted the connection properly, it could have slowly backed itself loose.
good luck,
David
