Does DSLR quality drop the higher the shutter count?

My Nikon D3100 shutter count is currently at 30,000. Photo quality isn't as great as I remember, but that might just be because I started using a Canon t3I more often and have let my Nikon sit doing nothing for about a year. Not sure if quality has actually dropped or if it's my imagination.

Does shutter count affect quality?

NO is correct

The only thing that will happen if the shutter starts failing is it my start overexposing the images (sometimes called shutter drag)

The photo quality has NOTHING to do with the camera you use. It has all to do with your skills using it.

Letting any piece of precision equipment sit for months or years is never a good idea.

30,000 shutter cycles is NOT a high number.

Quality is a direct function of using the cameras controls by the user, NOT the brand or model number of the camera.

No, but it is not a good idea for a new photographer to use two different systems.

No, on pure theory. If, however, the shutter loses it's ability to be controlled accurately, then of course your photo exposure is going to suffer. High shutter count does not necessarily mean an inaccurate shutter function, and an inaccurate shutter function is not specifically tied to shutter count.

No, but lens quality can deteriorate over time. It sucks because of how expensive they are, but it may be time for a new lens.

The shutter count per se will not affect quality. You may see inaccurate exposures as the shutter starts to wear but not as early as 30,000.
Have you had the sensor cleaned? Over time it will accumulate a film of grime that will degrade image quality somewhat.
Are your lenses clean? No internal dust or external grime?
Do you have a UV filter attached? Is that clean?
If you haven't done it already then maybe it is time for your camera to receive a clean and service.