If the old HDD does not spin, you probbaly cannot salvage the data. If it spins, but cannot be seen or its folders and files are not visible, you MAY be able to recover the MBR and the folders and files using
TestDisk. Do read the wiki, and it helps if you can install the old HDD into a working system to recover its data. You may also try the free
EaseUS Partition Recovery.
If the old HDD is still functional, you can download free cloning software from the HDD manufacturer's website. You can then use that to clone the old HDD to the new one. If the new one is larger than the old one, you'll have to use some free partitioning software to re-size the partition on the new after you've successfully cloned the old one. I have used the free
Partition Wizard and the free
EaseUS Partition Master.
I have successfully used all of these to manage HDDs and recover data.