I found the solution.

The problem due to the fact that before the upgrade the search index was on a different drive, one that was no longer available after the upgrade.

As soon that I changed the value of HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows Search\Gathering Manager\DefaultApplicationsPath to a path on the drive C: the Indexer started working perfectly. (There were other paths to fix, but the above is the one that would cause the service to fail).

Strangely enough, the path involved and the missing drive were not among the path returned by Process Monitor...

The problem is due to the fact that before the upgrade the search index was on a different drive. One that was no longer available after the upgrade.

As soon that I changed the value of HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows Search\Gathering Manager\DefaultApplicationsPath to a path on the drive C: the Indexer started working perfectly. (There were other paths to fix, but the above is the one that would cause the service to fail).

Strangely enough, the path involved and the missing drive were not among the path returned by Process Monitor.