After my hard drive was replaced I installed Mountain Lion. I was unable to use time machine or migration assistant to access files on my external Omega hard drive even though the files are still there? Is there another way?

My hard drive on my iMac was unrepairable so Apple installed a new one for me. When I reconnected my external Iomega USB hard drive I could "see" the original backup figures and the rows of "windows" and back to the original red rows of dates in time machine, but I could only access the recent installation date of my new OS X Mountain Lion. Migration assistant would not work as well only accessing the recent backups. Is there a way to "unlock" the past data so I can retrieve my documents and photos without resorting to purchasing "rescue" software??