Transferred Songs to second iTunes library, latest iTunes on latest Windows 7 - exact same issue - the Songs sit in the 'Purchased' playlist following download but do not show against the Artist and do not show as present when you attempt a Song search in iTunes.
This is very odd. In the file system the files are exactly in the correct position.
Remain in need of sage advice - how to remedy?
Right click each Song & select 'consolidate'; accept the action is permanent; the Songs now appear in search. Issue solved!
Not sure why this occured but the solution is effective.
The problem you saw is an intermittent but longstanding problem whereby the songs really are in the library, and do show up in playlists, but do not display in the Music list.
There are a few home remedies for the problem, but you have discovered a new one!