Yes, unplug the old drive to make certain the new HD is booting correctly. Then format it so it's no longer bootable. Then continue to copy your personal files onto it for extra storge and back-up.
My old main hard drive was too small and crowded, so I installed a new large one. The new drive is installed as a Serial ATA drive; the old one was the Master drive installed with the IDE cable. I used Acronis to copy the entire old drive content onto the new drive and checked the BIOS to make sure that the new drive is the 1st boot drive. Everything went well and I'm happy to have lots of storage space now. Bit by bit I've been deleting stuff from the old drive, after making sure I had it on the new one.
Here's the problem: Sometimes (not always) after a shutdown and reboot, the computer reboots from the old drive, calling it drive C. When I drecognize this, I go into the BIOS and reassign the boot order and restart. This is not a major problem, but it is a nuisance.
So here are my questions. (1)To try out the system without the old drive, should I just unplug it and see what happens? Or would it be better to go into the BIOS and disable it there? (2)Assuming that the system works OK after I do one of those, can I then reconnect/enable that drive and then format it?