When the red light starts blinking, how many times does it blink before it pauses and starts blinking again?
Then most likely what you have is either a new defective lamp (not likely, but possible), or the lamp power supply is defective.
By the way, blinking in 3 flash intervals means the lamp door isn't closed securely, but it looks like you don't have that problem anymore.
Are you at all handy with electronics, have a voltmeter, and would be comfortable taking the back off of the set? If so, I might be able to help you figure this out.
If not, then of course you're going to need a tech to help you.
Let me know if you'd like to try, and thanks for using JustAnswer!