No picture, no sound, does light the insignia sign. Why?

You can just buy a new remote. Test it using the smartphone front camera trick. Or it is the television that has no signal, do a Power Reset. Pull the mains plug for 5 minutes. Press and hold the power button on the set for 1 minute. Plug back in. Also check the input leads on the back for whatever is supplying the signal, Cable, Satellite, OTA, then check the Source button on the remote.

Insignia LCD TV Remote Control - NS-RC01G-09

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Start by testing power board voltages

in 90% of cases this is the fault of the backlight led, can only be repaired at a specialist service

Unfortunately your TV will need to be serviced. You may take the unit back to the retailer of purchase to arrange for repairs.

This television, appears to have had a failure in the mainboard. This is the board that controls the video functions and sound functions. The unit should be taken or sent in to a service center for testing and servicing. The service center will have all the correct service information to determine the problem for you. You can call Insignia customer support at this telephone number 1-877-467-4289. You can also got to the customer support website at www.insignia-products.com. Go to the support section and ask them for help on how to get service for your television. I hope this information helps you with your problem.

Both power supplies are supplying the same voltages to the circuits but in order to use the one from the NS-27LCD 27" you will need to change the wiring configurations to make it work for the LCT2715..
I could repair the power supply from the LCT2715 for under $90.00 including parts, labor and shipping it back to you.
Let me know if you require further assistance.

Does anyone know where can I buy a screen for a 27" LCD Insignia TV. Model is NS-27LCD? My screen creaked. I checked out e-bay and have not found a broken TV with a good screen. Does anyone know where I can buy a screen at. 
Thank you all for you time. 
JC 

I have a 26" Insignia HD-TV and just found out the cable remote code (to connect TV with the cable box) is 0463.  If that's not what you need, try calling Insignia's help line at 877-467-4289

I would replace the remote, you can buy an OEM remote at the link below. 1 800 Remotes