I just got an email from this forum with a comment that is not listed here. Odd...here it is:
Please check which files are supposed to be edited. The core rules goes into wp-content/cache/page_cache/.htaccess the other rules goes into the XXXXXX/.htaccess file.
I don't have a wp-content/cache/page_cache/.htaccess file. I don't even have a page_cache folder but I have a wp-content/cache/page folder. Should I create a .htaccess file in that folder manually?
If I disable the page cache the plugin tells me
Edit file
XXX/public_html/.htaccessand remove all lines between and including # BEGIN W3TC Page Cache core and # END W3TC Page Cache core markers.
which is quite different from the statement above. Totally puzzled now...