I have a RCA 42"

SOURCE: Black Vertical line appeared on my Daewoo Plasma

disconnect the set from the outlet to try to reset it, lets start with this if not provide model # and brand

good luck

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SOURCE: Black line on Panasonic Plasma

All lasma an lcd ts have boards that control vertical and horizontal output to their respective areas. They are connected to the screen by ribbon cables. If one of these boards fails all together, has a failed chip, a bad connection, or a bad ground somewhere it will result in a black line in the area of that board. A bad ribbon cable connection on the bottom will result in a vertical black bar though the screen. Many times reseating the connection will fix it, if the ribbon cable has been nicked there could be a severed connection. They an sometimes be fixed, but it is a pain. An yes I have done it, but the bar is gone. The same will happen if the chip that outputs to that area opens. The connectors are the first place to look paying close attention to the cable, they are extremely delicate so great care must be taken if you decide to tinker with em, the usually have lift locks that release them, but it is very easy to wreck em. Good luck.

SOURCE: no signal display on rca 42" lcd

If you have tried other input jacks and cables with the same result, then yes, the input/output board is defective or buggy.  Sometimes a power drain can clear this up as well so it's worth a try:
1. Unplug the product's power cable so the device is not grounded to the house. 2. Press and HOLD the product's own power button for 1 minute to drain the capacitors. 3. Plug the product back into a wall outlet and try to turn it on.
Note: This procedure works with battery operated devices as well so remove the batteries and hold down it's power button.  Electricity can remain in capacitors and on circuit boards enough to prevent normal functionality. By clearing the residue electricity, your product will have a fresh start and many times this will resolve a buggy or non-responsive device that appears to be dead.
If this doesn't resolve it, service would be necessary.

SOURCE: rca 42 in lcd it shuts off 5 sec after being turned on

This could be a power supply problem, these tv's use a series of switching mode power supplies usually mounted in the same circuit board , the light flashing is an indicator that this is the problem, but these boards are expensive so you may want to get the tv looked at before anything else. You do not mention if the sound remains in your description of the symptom, but just in case it does then a back light inverter could be at fault. hope this helps. thanks for leaving you feed back.

SOURCE: No picture but have sound

That click might have originated in 2 places: either it was the main relay disconnecting or it was the sound of a capacitor popping. Both are very severe problems - they signal that the power source of your tv has just failed.
Fixing it is a job for someone with electronics experience, if you're not one then call a repairman.