recently my imac of 7 years died.

I susequently purchased a new imac 2.9 intel core i5. My old imac had an external hard drive to which I backed up. Unfortunately, the new os, 10.9.2 does not recognise the back up which used the lion os. As a result I cannot access my previous files. Can somebody advise me as to a solution please.

Thanks, Hannes