The amber light on your television is more than likely the standby mode; very much like how your computer monitor goes off to save power, some televisions are designed to power down after a certain amount of time. Unfortunately, there are a number of potential issues with a television stuck in standby mode, including dry capacitors, loose or burnt out lamps, malfunctioning fans and broken circuit boards. Some of these repairs are easily addressed at home, while others can cost more than a new television.
Remove all connections and devices from the television and try turning it on and off again. If this allows your television to turn back on again, start connecting the devices one at a time to see whether it's a particular device or port that is malfunctioning.
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Unplug the television and let it rest for some time, anywhere from a couple of minutes to overnight. Plug the television back in and press the power button to see whether it turns on after getting an extended rest.
Consider replacing the capacitors. Some televisions that use standby mode instead of powering down have trouble with capacitors. They work until a sudden loss of power (such as from a storm or a blown fuse).
Listen for the noises for fans; sometimes televisions will fail to power up if a fan isn't working. You can choose to replace a fan at home, but make sure that your television is turned off and unplugged and that the fan you're using is going to fit in your television.
Slap the back of the television a couple of times while powering on; for some televisions, this can cause a faulty lamp or ballast to start working by jolting proper parts back into place. This method can also be a bit risky as it involves smacking an expensive piece of machinery, but it can provide a fix.
Consult a local repairman. Some televisions have trouble with power boards or other circuit boards. If your television is having trouble with a mechanical component, those pieces might need to be replaced. While you can undertake these replacements yourself, having a professional look at it can save a lot of grief.