The most common cause of an RCA TV failing to power on is a problem with the unit's power cord. Other issues may be due to problems with the unit's controls or internal power supply that may be resolved by rebooting the television.
The most common reason that an RCA television refuses to power on is that the television is not receiving any power, and the most common reason the television does not receive power is a problem with the power cord. This is often as simple as the cord having come unplugged, so checking that the cord is plugged in to both the television and a power outlet first is a good idea. It is also possible that the cord or power outlet is not functioning properly, so try plugging the television into a different outlet or using a different power cord if you have one that is compatible with your television handy. Also, try directly connecting the television to a wall outlet if it was previously attached to an extension cord or surge protector.
RCA televisions sometimes fail to power up due to internal problems. While these issues often require service, it is possible to resolve some of them by performing a "reboot" of the television. Unplug the television completely from the wall and let it sit for 5 minutes, then plug it back in and turn it on. If this does not resolve the issue, it may be necessary to have the television serviced.