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1. What is unit model?
2.Have you tried cleaning the flame sensor?Some of these units actualy use the igniter as flame sensor also.
Sounds to me like you have a bad board.Number one is because we should continue to keep voltage to valve unless a safety switch opens and number 2 if unit fails, the board should give us an error code rather than say all is fine.
I understand you just replaced board but that does not mean anything with the imported crap we get these days.Just changed mass air flow sensor out on my truck.Called after I replaced first one and asked if they had any more in stock I could try .He looked and said yep ,got another just like it in my hand waiting on you.He was right.Second was junk also. Took 2 parts before we got a good one.