I'm guessing you've got an ADSL connection through the phone lines (rather than fibre optic) and judging from the replies above, you've already checked the micro-filters.
Your internal phone wiring could be shot. A few simple tests come to mind:
1. Check that all phones connected in the premise are all connected through a micro-filter
2. Disconnect all phones and check that the internet connectivity doesn't have any further issues
3. Build on
#2 above and test your modem on all points
4. Disconnect all extensions from the master socket and see how your internet connectivity fairs up.
The reasons behind each:
1. Simple, your phone and adsl frequencies can clash hence the need for a micro filter
2. Just ensure that you don't have a dodgy filter, phone or extension
3. Try to rule out which section of your extension is shot
4. If the internal wiring is shot, then it could affect all the way back to the master as it's connected from the master. Best to rule it out - although this option should be a last resort as I don't believe this could really be possible.