You havent said what type of drive this is. I am assuming that by "hard drive" it is a actually a disk unit that requires both power and data connections. Specifically, its not a pluggable USB drive.
There are a few things you can check. Can you do a scan on the disks? There are two ways to do this:
ls /dev/sd*
sudo lsscsi
You may have to install lsscsi. It lists whatever is on the SCSI connectors to your motherboard. Don't fret that you will probably have used SATA rather then SCSI. For this purpose the two are synonymous.
Lets assume that you have a good electrical connection now, and that the drive is seen by the motherboard. It should, all things being equal, be the highest letter drive in /dev/sd* and thers should be a couple of partitions.
Next, we need one (or more) directories to mount the drive on. And we mount the drive. I am going to use the example /dev/sde1 as the partition. YOUR DISK MAY VERY WELL BE DIFFERENT!
sudo mkdir /mnt/disk
sudo mount /dev/sde1 /mnt/disk
The other thing you have not shared is how this drive was formatted. I am assume is ext4, or similar, and not one of the exotic formats. If it is an exotic format that is not known to you Ubuntu setup then it will need the drivers installed.
One thing to note: taking a boot drive from one machine to another, and expecting to boot from it, is going to be tricky. The boot and OS installers add a number of firmware bits of code that are specific to the CPU and motherboard. It does this silently when the OS is installed or upgraded. Unless your motherboards and CPU are identical, booting from another machines harddrive may cause issues.