I will make a VERY hesitant guess but a cheap one to test, since you have one combination which does work: one of the ADSL filters is bad. Or, if you don't have a little box thingy on each of your phone outlets, you don't have an ADSL filter.
I suggest you buy one, connect up the one solution you know works, but this time via the filter, and see if you can still connect. If you can, it's a filter woe.
(I hope I'm not teaching anyone to suck eggs here. The high-frequency ADSL signal is piggy-backed on the low-frequency phone signal. At your end, you need a filter that splits off the signals, so the modem only sees the high frequencies, and the phones only see the low frequencies. The boxes are small and very cheap.)