You don`t say how many `phones you have and whether the PC is on the master or slave socket. If you are on a slave, how far is it from the master?
The high pitched bleeps may be the PC attempting to connect and the fact you can hear it on the `phone indicates to me that a filter may be failing/not up to scratch.
I would suggest you disconnect all `phones and filters and, if possible, connect to the master socket. If the problem is resolved, reconnect your filters and `phones one at a time and see if the problem returns and at which point in the connection process.
If all works fine, repeat the process from your normal PC connection socket, again checking to see if and when the problem returns.
If a piece of equipment (`phone or filter) appears to cause the problem, it may need checking out. For a filter you can try it on the master and add a known good `phone to eliminate the filter and reverse for the `phone.
If everything is fine from the master and the problem is only on the slave you use for the PC, you may have a wiring/distance problem in the house. If the wiring and distance from the master are within limits it would appear to be with BT. Unfortunately they would probably want to confirm integrity of the house wiring at your expense (if the problem is found there) but at least you will be armed with some investigative work to start with.