Hi chi and grahack,
Thank you for your replies.
1. I turned the Use Nice URLs option off, but still no luck.
2. Yes, images are on the server.
3. I didn't change anything at all.
Kind regards,
Dmitri
Edit: I can see that the problem affects not only images, but all files stored in the media directory. For example:
http://www.nothickmanuals.info/doku.php/cheatsheets
I can't download any of the available PDFs.