Often the BIOS for your motherboard on your system will default to having the optical drive as your primary boot device, it's good practice to get into BIOS regardless of an old or new boot drive and make sure your primary boot device is the HDD/SSD in question.
Can you please pass on your full system's specs in case you might have missed something? Do note that entering BIOS can be achieved by tapping on the DEL, F2 or F8 keys depending on your motherboard make and model.