Well it sounds a bit like DNS, yet if you can't ping all the time it would suggest other problems. Firstly I'd contact IDNet and discuss any of the problems. I doubt its likely to be a pronlem with IDNet as it hasn't been across the board, so its likely its just your end. The fact that the PPP and Line is still connected lead me to believe the main fault is coming from the router, so it would be a good idea to contact BT and RMA if you can.
Would also be worth checking wiring, but it's unlikely to be due to that.