So I had a client site that was running 1.5.22 and got hacked (mailer.php spam hack) and needed to be updated.
I tried many fixes that were recommended in Joomla forums, none helped.
So what worked for me to repair admin menu not working after update?
1. Created a clean install of Joomla 1.5.26 in DirectAdmin (simple, few clicks)
2. Copied clean install folders (with everything included) over my working website (which I backed up first).
Specifically, I selected these files and folders:
Hope this works for you too.