The filter (the lil box in wich you connect phone and modem) needs to be plugged into the first "phonesocket" in the house so it can route internettraffic to your comp and phonetraffic to your phone. If the phone is connected before the filter then yes your internetconnection gets lost..remember at that point it only knows phone.
If the modem cable isn't long enough, go to a computer/electronics shop and buy a longer one (they sell them from a roll). They can also put the lil plugs on for you or you can do that yourself with a special tool for it.