. Ideas we have, a solution...maybe.
Try going into Disk Management (Start/Run...type diskmgmt.msc and hit Enter.
Do you see the new drive listed in the lower portion of the screen?
If so, tell us what data is reported in that section of the screen for that drive.
If so...try giving it a drive letter like W, rather than whatever appears to be assigned. If that drive has a permanent letter assigned that is already in use by another drive/partition on the system...it cannot appear in My Computer/Explorer until the drive letter is changed.
Although I don't think this applies...an unformatted drive will also appear properly in the BIOS but cannot be recognized by My Computer/Explorer...until it is formatted FAT or NTFS.
There is still another possibility...the jumper setting on the drive needs to be changed to match the connection that you have made on the new system. If attached to the end connector of the IDE cable, set it to Master or CS...if attached to "middle" connector, set it to Slave or CS.
The waffling about jumper settings...comes about because both drives must use the same set of settings. If one drive on the cable uses CS (the default setting on new purchased drives), then the other drive must use CS also. If one drive uses Master/Slave, then so must the other drive...with the Slave setting applying only to the drive connected to the "middle" connector.
Those are my best guesses for now.