Booting the new system using the old HDD, is highly unlikely to work & if it does, it will probably be very unstable.
You will need to do a fresh install of the OS on the new drive instead.
Copying programs over from the old drive to the new is also highly unlikely to work.
The best thing for you to do is this :
Do fresh install of OS on to new HDD & install any programs that you need.
You can add the old drive into the system by setting it to be a slave (jumpers on rear of drive, new drive must be set to master).
You can then attach the old drive to the same cable as the new drive (place new drive on end of cable, old drive in the middle)
You will then be able to access any of your own files (eg, docs, mp3 etc) that are on the old drive, & transfer them to the new one if you wish.