How long have you had the set for, and when did the problem occur?
Additionally, what is connected to the TV for devices (DVD, cable box, etc.), and do you have the same issue regardless of which you're trying to watch?
Also, if you press the MENU button on the TV remote (not the cable box remote), does the MENU come up on screen?
On the TV itself (no remote), press either the INPUT, Menu, or Volume buttons, do any of these indicators come up on the screen?
Additionally, are there any blinking lights, buzz or hum sound on the set?
Do you have a DVD player or other device you can connect to the TV to see if the picture comes up right away?
Also, when the picture does not come up right away with Direct TV, does the TV still have sound?
Yes the symptoms you're having are extremely common with a lamp that is failing. The filament will change resistance and cause the ballast to become unstable and shut the picture down, with is usually cured by a power reset until the lamp finally fails completely.
The link below is to where you can purchase the lamp for your set:
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Average life expectancy of a lamp is around 2-3 years, whish is right in the range you're in.
The link below is to a free download of the manual. Instructions to replace the lamp yourself, are on page 64: