Except for cable, all broadband goes through BT, so there is no point in changing. The fault seems to be with the modem not the supplier.
I would ensure that the modem is well away from speakers and electrical apparatus (placing it on the top of the tower case is not recommended). I have also found that plugging ADSL USB modems into USB extension boxes can also cause problems, so make sure that it is plugged directly into the USB connectors on the PC case. You could also try placing the modem on a small piece of rubber matting or latex matting.