An ExpertFlyer subscription would be very worthwhile, as you can easily find availability for each segment. As said above if there is no A/D/L fare bucket availability you will not be able to book.
I find EF the best way to get base fare for various starting points but a pretty tedious way to search availability. I prefer to use ITA which can be told to restrict look ups by airline and/or fare basis (e.g. L, D or A).