If you have extended the mic cable using a 4 twisted-pair network cable (CAT 5, CAT 6, etc), take it out of the picture and connect the microphone directly to the radio using the supplied cable from Kenwood.
There is a known issue with the TM-V71 and TM-D710 radios and their mic cables. In addition to microphone audio, there is a pulsed clock signal going through the mic cable. The Kenwood cable shields just the mic audio line and leaves the line carrying the clock signal outside the mic audio shield. Twisted-pair network cables often have no shielding at all and depend on the twisted pairs to reduce the common mode interference. But, the pin-out of a typical network cable puts the line carrying the clock signal in close proximity to the mic audio with no shielding.
Even if your mic cable isn't picking up the clock signal, it could also be picking up RF generated by the radio. To mitigate this interference, your antenna needs to matched to the transmitter (low SWR) and your grounding needs to be in good shape.
Also, if your installation puts any kind of strain on the connectors at either end of the mic cable, that strain might mis-align the RJ45 connectors resulting in less-than-perfect contact. Make sure that the connector plugs straight into the radio with no pulling to either side or straight out.