Your old HDD has drivers for the old machine so it won't run well -- probably BSODs. Your new HDD cannot access the programs because they are installed to the old HDD and all the registry entries for them are absent on the OS that is running on the new drive. Best thing to do is re-install the programs on the new HDD.
edit: then after that I would move all the data off the old drive and unpartition it completely (get rid of all HP partitions you no longer need since the machine is dead) and then reinitialize/reformat it and use it as a data drive.
My older HDD is only about 6 months old. It's a 1.5TB Seagate drive. It is not partitioned. Do you still recommend the same advice after those facts? Thanks!