Do NOT try to boot up from the old HDD in the new machine. But you should not need to. IF that old HDD is OK and only has corrupted Win 7 files on it, the new machine with Win 8 certainly should be able to access it.
You need the old HDD mounted and connected (to a SATA port I presume, because I'm guessing all your drives are SATA) in the new machine. When you start up, go immediately into BIOS Setup and check three things.
1. Does the old HDD actually show up properly in BIOS Setup - that is, is it detected correctly?
2. Check the SATA Port Mode for that unit. I suspect your new machine with SSD and 2TB HDD is set up to use those units (and maybe all SATA units) as AHCI devices, and NOT with the IDE Emulation setting. Now, do you know: when the old drive was in your old machine, was it set to be used as an AHCI device, or did it use IDE Emulation? If you KNOW that answer, and if you can actually change only that one SATA port's mode, make it the way you know it should be. (You do NOT need it set to "RAID".) But do NOT change the Port Modes for your new SSD and 2 TB unit - leave them as they came.
3. Now go to where you set the Boot Priority Sequence. It may be set to boot first from your optical unit, and then from the SSD that has your Win 8 OS on it. But the sequence should NOT have your old HDD anywhere as a possible boot device.
IF you change anything in BIOS Setup and want to make that permanent, remember to SAVE and EXIT. Or, if you decide you don't want anything changed, just Exit without Saving.
OK, so now your machine boots, but you still can't find your old HDD in My Computer. You even say you can't find it in Disk Management. Go back there and look closely this way:
Any HDD that was successfully detected in BIOS should show up in Disk Management, but maybe only in one place. On the right are two panes. The top one shows you all the devices Windows CAN use right now. But look at the LOWER RIGHT pane, which also will show you any valid hardware storage devices that BIOS has detected, but Windows still can't figure out. NOTE that both panes SCROLL so you can see all they have. Find your old HDD.
Now, what does it show? The HDD will be represented by one large horizontal block. At its left end will be a bit of info about the HDD itself. To the right of that may be one or more sub-blocks, each representing one Partition on the unit. A Partition is a chunk of space that Windows will treat as one "drive" with its own letter name. If there is any space on the drive that is NOT part of a Partition, it will be labelled as "Unallocated Space". In each Partition there will be some information: a disk name given at the time of Formatting like "MyDisk", a letter name in brackets like (E: ), a "drive" size in GB, a File System like "NTFS", and a status note like "Healthy".
So, what do you see there? If it all looks good with an NTFS File System and a letter name, it should also show up in the Upper Right pane. If it does, back out of Disk Management and check again in My Computer - it should be there.
BUT if the File System is NTFS and there is no letter name in brackets at the end of the first line, you can fix that. RIGHT-click on that sub-block and choose to assign a letter name - not one already in use. If you do this, back out of Disk Management and reboot to allow Windows to update its Registry. Then check My Computer.
BUT if the File System says it is "RAW", there is a bit of corruption in a Windows system file on the drive and Windows can't read it properly. This becomes a data recovery problem, and assigning a letter name will not do the job. If that is your situation, post a note here for further advice.
If you get it working, let us know what you found. If not, post here what you do see in disk Management's Lower Right pane so we can help more.