I agree Slartabartfast. I'm stumped as to what caused it. I initially thought it was only on one track and thought maybe a cable or mic issue, but that does not make sense on two tracks and only when there is signal present. I would like to figure out what the cause was.
Jackson

Is any plugin in the relevant drum tracks getting overloaded and distorting the audio?

Might be worth turning off all eq and fx on the tracks and muting any sends they have to see if that makes a difference. If you've only noticed the noise right at the end of the production process that makes me wonder if it's present in the original recorded audio or a consequence of something done after it was recorded. Might even be worth re-loading the original unprocessed recordings into new, plugin free tracks or playing them through eg media player just to see if they are "clean" or not.

No matter how good  I don't think a noise reduction plug in will help much. 
 
My approach would be to open the tracks Wave file in a wave editor as that would rule out all other interference. 
If the noise goes away you are saved because now all you need to do is find the cause from with in Sonar.
 
If the noise is still there. My first move would be to open a back up of the original recording. 
If the noise was there from the beginning and you just missed it, my next move would be to replace this track using one of many tools we now have on hand. 

Both Izotope and Accusonus ERA-D worked. I chose Accusonus ERA-D this time, but will be purchasing the Izotope Rx Pack for future emergencies. Thank you to all who responded. Lots of good information here.
Jackson

You made me curious as to what caused the issue, perhaps this was a Tube Guitar Amp? 
 
 
In electronics, motorboating is low frequency parasitic oscillation (unwanted cyclic variation of the output voltage) that occurs in audio and radio equipment and often manifests itself as a sound similar to an idling motorboat engine, a "put-put-put", in audio output from speakers or earphones.[1][2][3][4] It is a problem encountered particularly in radio transceivers and older vacuum tube audio systems, guitar amplifiers, PA systems and is caused by some type of unwanted feedback in the circuit. The amplifying devices in audio and radio equipment are vulnerable to a variety of feedback problems, which can cause distinctive noise in the output. The term motorboating is applied to oscillations whose frequency is below the range of hearing, from 1 to 10 hertz,[3] so the individual oscillations are heard as pulses. Sometimes the oscillations can even be seen visually as the woofer cones in speakers slowly moving in and out.[2]
Besides sounding annoying, motorboating can cause clipping of the audio output waveform, and thus distortion in the output.

Interestingly, no amplification...  drums mic'd direct into a mixer into the DAW...  it's weird...

https://www.youtube.com/watch?v=sctKIMAunhk
 
This is me trying to remove some noise.