40" Samsung wont turn on

The gradual death you describe is probably caused by the decay of an electrolytic capacitor in the main power supply. It would require a capacitance meter with loss measurement to ferret out the bad part. Eventually, the supply will fail to start at all and leaving it on will cause the weak part to decay faster.
You might want to do some advance research on the cost of a replacement supply which you can probably replace on your own. These are normally on a separate board that will be visually related to the AC coming in and will have larger than average components on it. For safety, leave the AC disconnected overnight before you start doing any surgery; the power supply can deliver a nasty shock if not allowed to discharge.