1. Have you moved the Rega and Rotel to the PC in a different room or is it all in situ in your living room?
If you've moved it it could be a mains outlet problem. Try using a different socket. Also make sure you keep your audio leads well away from any mains leads on the back of your PC.
2. Does the hum only appear on the recorded output or can you hear it through the PC speakers when it's playing?
3. Is the hum on both channels, stereo, or just out of one side, mono?
4. Do you have a sound card or is it a chip on the motherboard? If it's a card try using a different PCI slot.
Also, make sure that your connections are solid. Try wobbling the plugs to see if the buzzing is intermittent.
5. Can you adjust the input volume? It might be set too high so it's picking up all the white noise in the signal and amplifying it.
jW will have some more info about this I would imagine. Earthing for example. I'm sure he'll be happy to oblige as he's extremely bored at the moment. He might even jump on a bus to fix it!
Good luck