Why won't Migration Assistant recognize my old Time Machine backup? When I attempt to run Migration Assistant, it searches and searches but can't find the backups. When I open Finder, I can clearly see the backups and navigate around in the backups for the different dates.

It's on an external drive (attached via USB, both during backups and now for Migration Assistant). The drive is formatted as case-sensitive, journaled HFS+. The backups were made from a case-sensitive MacBook. I recently replaced the HD (the old one failed) and I'm attempting to restore my files to the new drive, which is formatted as case-insensitive.

The laptop is a late-2008 MacBook (unibody). I just upgraded the stock HD to a 7200 RPM Wester Digital w/ 750 GB. The external drive is a 1TB LaCie w/ 2 partitions (a FAT32 for wife's Windows box, and the case-sensitive, journaled HFS+ partition I'm using for Time Machine). I'm running the latest Mountain Lion (both before and after the HD crash).
Seems that many people have difficulty restoring from a backup of a case-sensitive installation to a case-insensitive one.  Please see comments for some discussion and various ideas.

A work-around which seemed to be successful in this case: copy the data you need manually from the backups, using the Finder. (I wouldn't expect to be able to recreate the entire machine with all settings etc this way, but documents should be easy to restore this way, and perhaps even your entire home directory.)