No longer have a 300 to check, but:

1) Put "Times New Roman" in quotes;

1a) put "!important" at the end

pre { font-family: "Times New Roman" !important ; }

1b) oooh, try this

pre { font-family: "Times New Roman",serif !important ; }

and see if it falls back to whatever its default is;

2) check how it displays in Sigil or the ePub reading addon for Firefox,

3) if it's showing as TNR in those then there's some problem with the 300 that I would have to look further into.