Hi.
I am experiencing the same problem as you are. And i have spent an unreasonably long time searching for a solution so when i came across this thread i had to create an account to spare you the time of figuring it out yourself.
Ok. Your problem could either be in your tv or in your mac. I myself have a Samsung LE40M87 which has a bug in the firmware that basically doesn't tell the mac what resolutions it supports. I'm not sure if this bug applies to your tv as well but it might give you some peace of mind to check that out first.
So i bought a Mini-DVI to VGA adapter, since the Mini-DVI to DVI to hdmi didn't work out that well for me. And i got the same reaction you got. The blinking blue thingy. And as it turns out (as I understand it).
In the Mac OS X 10.5.7 update something was rewritted or changed in the driver or code that does the hardware scan. I have read tons and tons of threads about people complaining about this, altough most them still had tv connectivity but the resolution scan was incorrect. But with alot of samsungs it seems that the compatibility issue made the output go away entirely.
You wrote that you just bought the adapter and cable so i guess you never tried the output in 10.5.6. (Nor did I)
Since we're in the same boat you and I i will go ahead and give you the same options I have.
1) Downgrade to 10.5.6 (no easy way out. re-install mac os and only apply combo-patches up to 10.5.6)
2) Wait until this issue is fixed from Apple. They are well aware of it but it might still take a while and there's no real guarantee that it will work with the older 3,1 macbook.
***** huh? ;(
Staffan