Sharp AQOUS 42 tv will not turn off and displays the Sharp logo and the screen goes black, like it is transitioning, but never transitions to another screen. How do I fix this and what is the issue?

Fault at its main digital board. Short circuited component/s at it. Contact any service technician; or the authorized service center. If you wish to get some details; check the site linked here. Surf the site with patience. Pull up older posts.
http://electro-medical.blogspot.com/

In most cases, the main board might have to be replaced. If so, a software [firmware] update too might be necessary.
Before going further; try a hard reset first. If it does not help you, replace the main digital board. There are two methods to reset TVs. The first is simple to do; a Hard Reset. The other is somewhat skilled; is a Factory Reset (System Reset). To make it a hard reset, just unplug the TV from AC mains wall socket, and re-plug it back after 15 minutes or so. If you do this by overnight is better. This procedure will make it a hard reset. If you want to make it a system reset [Factory Reset]; you have to enter its service mode option, and select the factory reset option. If you wish to get some details; visit the site linked here.