Several things could be to blame for your problem.
Have you any idea of the distance you are now from the local telephone exchange...if you are some distance away your modem may be struggling to maintain the signal. If you go to click here? this will give us a rough idea.
Is there any way you can try the connection from the Master telephone socket or preferably the test socket underneath the removeable faceplate if you have the new style NTE% type socket. If you can get a signal from there it could indicate there are problems with your internal telephone wiring. Follow this guide click here to check your internal wiring is in order in any case.
You say the line seems clear when you remove the filter, this could indicate a faulty filter. If you were on a nice short line to the exchange at your previouos house this won't have mattered that much but could make a difference now. Just to clarify, you only need a filter on each socket if another device is connected, i.e. telephone, fax, Sky, burglar alarm, if the modem is the only thing using the socket you don't need a filter.