Slow internet speed due to PC interfering with BT ...

Question

In July I bought a Medion desktop PC from Aldi. From the outset I had problems getting it to work reliably with the Internet. When the PC was switched on the download speed would be about 14Mbps, but it would gradually deteriorate until it stopped working altogether, and it would also slow down the rest of my network. This was the case using either wired or wireless connection. BT support weren't interested as all my other devices (two laptops, Nexus 7, and iPhone) worked perfectly as long as the Medion PC wasn't connected. They said the PC must be faulty and I couldn't argue with this. I became convinced that as the problem got worse after the PC had been switched on for some time, it must be a thermal problem in the PC. Support from Medion was useless, so the PC was taken back to Aldi for a refund.
Last month I got a new PC from a local shop that custom-builds PCs to your spec. When I got it, lo and behold it had exactly the same problem, although it worked fine in the shop on their (non-BT) internet connection, and also when the owner subsequently tested it on his home network. I also noticed that the problem occurred to a lesser extent (slowing down other devices on the network) if the PC was switched on but not connected to the Internet, with both wired and wireless network adapters being disabled. This makes me believe that the PC is generating some interference to which the BT Hub is susceptible.
It's pointless trying to get support from BT as they will just use the same argument, (other devices work fine so it must be the PC) - but on the other hand, the PC works fine on other Internet connections.
The PC has an AMD 4 x 3.8GHz processor. The PC and Hub are in different rooms about 20ft apart.
Has anyone experienced a similar problem and found a solution? Would a later version BT Hub be any better? If the problem isn't resolved I am going to switch back to Virgin when my BT contract runs out. 

Answer 1

Thank you very much for your suggestions. I did some experiments and got some interesting results.
The monitor isn't the problem, completely disconnecting it made no difference. The interference is definitely being carried over the mains. Per your suggestion, I tried leaving the new PC in its existing location but connected via an extension lead to the cooker socket in the kitchen, a 40A circuit close to the consumer unit. With the new PC on but not connected to anything, other devices on the network are fine. However, connecting an ethernet cable immediately screws things up, so the the ethernet cable is also acting as a conduit for the interference. Wireless on the new PC seems to work but it and the rest of my network are still slow, fluctuates between about 7Mbps and 10Mbps v 14Mbps normally. 
I'm not sure if this is going to lead to a practical solution because:
1. Can't run a permanent cable to the kitchen!
2. Speed is not brilliant, wired still doesn't work on new PC.
3. The new PC is being configured in the spare bedroom, but must ultimately replace my old PC in my office. This is where all the ethernet cables on my network converge and where the BT socket is, so the BT Hub must be in the office as well.
4. All PCs are already connected to mains sockets via filters/interference suppressors, so I don't see what else can be done to reduce mains-borne interference.
Having identified the root cause of the problem, any suggestions for a permanent solution that would let me have my office set up as I need it would be very welcome.