The problem you have with this file is that there are font-family statements at a "lower level" than body or body.calibre.
You should be able to correct the already-converted epub by amending the epub's css file in Sigil or with Tweak-epub in calibre (whatever you're comfortable with). Given the settings in your @font-face statements, there is more than one way to fix this but the following 2 steps should work:
1. Change all those instances of
Code:
font-family: "Times New Roman";
to
Code:
font-family: serif; (or font-family: "Liberation";)
and all those instances of
Code:
font-family: Arial;
to
Code:
font-family: sans-serif; (or font-family: serif; or font-family: "Liberation";)
I don't want to confuse you but I feel I should also add that the above could also have been achieved via the original Calibre conversion to EPUB if the Calibre ExtraCSS had matched your source file. I can't see the source file so I can't tell you what it should have been. If you want to pursue this for future info, send me a PM and we can take it from there.
2. You also need to make sure your actual font files are in exactly the correct directory as specified in your @font-face statements. e.g. you have referred to the Regular serif font as
Code:
res:///Data/fonts/LiberationSerif-Regular.ttf
which means that looking at your Sony in your PC's file browser you should have a directory
containing the file
Code:
LiberationSerif-Regular.ttf
Everything is case-sensitive so directory names, filenames and extensions must match EXACTLY.