My Samsung led tv model number un60eh6003f is turning on but it has no picture

Hi Robert
By "no picture" I would assume you also mean no menu or anything. A dead screen.
There is not much that you can do with a modern LED TV as it is really a computer internally. Memory & Timing Controllers. See if you can find a reset button or small reset hole on the back. (See Your Manual).
Like a computer there may be certain keys that you can hold down on power up that cause it to reset it's internal CPU.
The Switch Mode Power Supply (Unit or PCB), which is often the cause of many problems. This usually stems from Heat & Leaky Electrolytic Capacitors in the Power Supply. So, if it's dead from lack of power to the various circuit modules from the switch mode power supply then this module can often be replaced with a spare part. You would need to check the internal switch mode PS output with a voltmeter if you want to go that far,
Hope this Helps

Fault with its main 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://electronicshelponline.blogspot.com/ . In most cases, the main board might have to be replaced. If so, a software [firmware] update too might be necessary.