assuming your old hdd still works AND the new system has the correct connector on the MB for the old hdd(probably ide 40 pin), then yes it IS possible to connect it in the tower,(BUT if it isa latop the ONLY option is an external hdd case for the old drive which is the alternate if the MB does not have the correct connector.
and all of theis is JUST to read the files from the old HDD.
harpo