The problem started when I noticed that some icons were missing from the Styles and Formatting and the Advanced Filter windows (in Calc). No worries, I said. I'll just reinstall everything.
After downloading Portable Openoffice and deleting the directory on the USB flashdrive and copying the fresh download there, the program wouldn't start. There was an error that icuuc26.dll was not a valid Windows image and that I would have to check the installation diskette(!). After copying that file to the USB drive, the same error appeared about another DLL. Then, nothing.
I searched for this error on the Internet, but I didn't find anything useful other than the fact that it's a Windows problem. Needless to say, I restarted the computer, redownloaded the application files, reinstalled it, but again with no success.
After more attempts I decided to install it on the hard disk: Portable Openoffice worked correctly from the hard disk. So, what I did was to edit the bootstrap.ini and copy the whole directory structure to the USB thumbdrive. Strangely(?), this solution worked.