Another thing to do is get BT to check that there is no kind of fault on your line. Don't be fobbed off with that quick test they do for a few seconds over the phone, it doesn't necessarily show up a fault. We had similar disconnection problems to you a few months ago and it turned out, when they did a physical check on our line, that there was a fault, which they repaired. Unfortunately, in our case, it didn't solve the problem, it was something else entirely which won't apply in your case with a new PC.
Madeline.