No power when switched on . Insignia model ns-27lcd

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Jason, this does sound like a main unit issue...although not 100% certain. Give a company named ShopJimmy.com a try for parts. They have been a huge help to me in the past. I included a link to your model page from their site. Hope that helps!
http://www.shopjimmy.com/catalogsearch/result/?q=NS-27LCD
[email protected]

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.

In about 90% of the time the power supply is defective if the TV fails to power ON.
I repair these power supplies, if you need further assistance write to [email protected]

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.

Try this Link.
http://www.usa.denon.com/ProductSupportAndArchives.asp

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

The problem is most likely the fuse connected to the power wires. You have to take apart the TV and follow the power wire to the fuse. Fuse number is T4AL/ 250v. It will be labeled above the fuse. We had the same problem. Also, check to see if the metal around the tops and bottoms of fuse are loose.
The way we fixed it was to wrap aluminum foil around the fuse and put it back in. It is only a temporary fix until we can get a fuse. Hope this helps.