Plug a light into the electrical outlet - does it work?
If not, check circuit breaker/fuse or light switch (switched outlet)?
Check the plug on the back of the TV - is it securely inserted?
Does the TV make any sound?
Are you pressing the power button on the remote or on the TV? - Try the TV.
If the remote, check that the batteries are inserted/properly.
Make sure you've selected "TV" on the remote and not some other device.
Usually when a TV is delivered, they unpack it and test it so that it's not DOA.