There was a check engine soon light on and then.

There was a check engine soon light on and then a week or so later the battery died and was jumped twice. It does not hold a charge for more than a few blocks. It sounded like an alternator but then we had it towed to a mechanic they claimed that they put it on the machine and it said that it was not drivable. They said that we have to get the key mechanism to connect with the engine and then they will be able to tell if it is the alternator. It is already a quote of 600.00 including a new battery and then if they have to replace the alternator it is another 414.00. Can there be any way to inaccurately record or quote the codes? Iwill donate if I receive quick and good info.