Sounds like more than one thing unfortunately...
The image on your TV is created by scanning a beam across the screen... 4 coils are responsible for that in the back of the TV. They are a form of electromagnet that rapidly change to direct the beam in a scanning pattern across the entire screen. If there is a white line... that means that 2 of the coils are not operating. This in itself could be caused by a couple of things. The direction of the line might help.
Now that all you get is a flickering power light... it is apparent that there is an additional problem, or that the initial problem got worse.
In order to scan across the TV fast enough, the voltage fed to the coils is incredibly high... Dangerously incredibly jump through the air and hit you high. The coils are driven in pairs, if one of the coils is bad, it could cause the circuitry that creates and controls that high voltage to fail as well. It could be any part of that circuit down the line. The fact that you had the line in the first place though makes it seem as though at some recent point in time some of the circuitry worked.
Now here's the kicker. I won't help you fix it. I won't give you tips, or recommend tools. I would suggest you don't even open it.
Remember that oh so very scary high voltage I was telling you about? It's not 110-220V that goes into the TV... there is a transformer inside that pumps out 1000s of volts, and this is the deadly scary sir gap jumping voltage that is incredibly dangerous to work around/on/with.
Go buy a new TV, or pay a qualified repair guy to take a look for you. It's not worth the risk to save some cash.
Best of luck
~Jerid