When the engine runs, unless the belt slips, it drives. If it was slipping it will most likely show signs of overheating etc. What you have described is characteristic of an over-age or over-worked belt, but if they slip you should be able to see some signs of it on the sides of the belt. It takes a lot of slippage to keep the transmission from working. You may possibly have a transmission failure - I think you need to talk to someone who has experience with the particular type of transmission, because it is expensive to replace, but some types are not repairable.
