bmann- I'm experiencing what sounds like the same issue and wondering if it may be a board issue. Also looking for answers so I don't buy parts I may not need. To add a little more to what you describe...
4 or 5 yo Samsung HLT5075S
On my 3rd bulb and 2nd color wheel - did the work myself
First time I experienced this was a few weeks ago, but now experiencing this consistently on almost every initial power on
Power on the unit and don't hear the melody.
Green light flashes.
Lamp comes on (screen is dark but is lit, lamp shines bright through back panel.
After a couple of minutes, it powers itself off.
So far, every second attempt results in a successful power on (melody, picture, etc), but not confident that it will continue to always do so.