It's likely this is not going to be an easy fix but to be sure, please try this:
-unplug the tv POWER cord from the wall outlet.
-press and hold the power button on the tv (not remote) for 20 seconds and release.
-plug in the tv power cord and try to turn on.
If that doesn't help then the tv needs diagnosis, parts, and service.
As a technician, theoretically I could help you with that but I actually would not recommend you repair of tv of this age due to the high cost of parts/labor and probability of more internal failures. But you saved a lot of money by coming here first- typically repair shops charge $99 up front just for diagnosis (to hand you an estimate).
Despite the bad news, I hope the answer I provided so far was satisfactory. If you need more help or don't understand something use the REPLY option.
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