Are you saying you removed the original 60GB HDD and replaced it with the 120GB HDD in order to format the 120GB drive, then switched them back?
I believe the PS3 uses a proprietary filing system format for the internal drive, and not FAT32 which it needs for recognizing an external drive. The reason for that is the need for copy protection on the internal drive, where copy write material is stored. If so, that may be the reason why both your PC and PS3 won't recognize it as an external HD... because you have formatted as an internal drive, and not with the FAT32 file system.
However, this is just a guess on my part, so it might be something else.
EDIT: At this point, I would recommend reformatting your 120GB HD to FAT32 using your PC, then connecting it to your PS3, unless of course you want to replace the 60GB HDD. In which case, put the 60GB HDD back and use the PS3's Backup Utility on the 60GB HDD. Then put the 120GB back inside, and restore your backed up data.
If you don’t want to use the 60GB HDD as a swappable secondary internal HDD for your PS3, simply reformat it with the PC to FAT32 and use it as an external HD. 👍