I think you have two problems. The first comes from running the balanced output of the DMP3 pre-amp into the unbalanced inputs of a PC soundcard. The second is due to the lack of ground continuity through the external power supply of the DMP3. You could fudge the present system or you could tackle the problem more radically.
You could help the first problem by using an attenuator between the pre-amp output and the soundcard inputs. The hum level would be reduced by roughly the amount of attenuation. A 12dB balanced attenuator could be used with unbalanced outputs and give you a better signal than what you have now.
For the second problem, I would take a separate earth line from the pre-amp ground to a good mains earth. Any ground-loop hum created by this will be much less than you are getting now.
The proper solution is to use an external audio interface instead of your PC soundcard. You should look for an interface such as the RME FireFace400 that has genuine balanced line-level inputs in addition to any microphone-level inputs. This is so that when you continue to use the DMP3, its output is not coloured by being attenuated and put through the microphone channels of the interface. You would not need the attenuator, and the whole system should not have any issues with mains hum even without the separate earth line.