I went to turn on my Samsung a little bit ago, which was working earlier today, and now it won't turn on and is making a clicking noise. The noise does not stop until 10 seconds after I unplug it...

Ether bad compressor our bad start kit on compressor.

that item is called a relay switch. it toggles on and off depending on which electrical component it is connecting. if it's blown, they are cheap and easy to replace like a fuse, but you'll need to look at the fuse box chart (usually on the underside of the lid) to determine which one and where it's located. You can't look inside the relay to determine if blown, but you can replace them one at a time to test...
Also, if you're experienced in electrical, a paper clip can be used when the relay is out, to connect the circuit that you need. use tools and or gloves when attempting this method.

sounds very much like the bearing has seized on the drum.
can you turn it by hand?
I'm betting it's either stuck or REALLY stiff

Clicking noises may mean a power supply voltage is not staying correct or that board is bad---a suggestion: visit shopjimmy.com who has by model number a list of all the boards used in almost every Samsung Flat screen set made.

try to boot the computer in safe mode with networking.

It could be the wheel bearings, does it make more noise when turning left or right?

Now tv turn on.Hear alots of clicking or squiling,loud motor noises turn on?Alot of clicking,the Ballast board it dead,this board help ignite the projection lamp.Tv also have a colors wheels.The colors wheel is dead,if hear squiling noises,loud motor noises.

ignition switch,,or,,battery dead,,or ,,broken wire at starter

the screen is dead, take it to your local cell phone service provider