My Sharp LC-60TQ15U is behaving weird for a week, it switch on via remote and then stop responding to remote. Suddenly menu comes and selects picture settings on its own.

Main system control memory IC fault. This is a very small IC; have 8 solder terminals, and can be located very near to the main system control-chroma IC. Check and replace it. Be sure to replace it with the same number printed on it; in all respect. Otherwise, it won't go. http://electronicshelponline.blogspot.com/ Before replacing it, try a reset to this set, and then check.
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; check the site linked here.