I have a T430 with the same issue. LEDs (power Fn F3 ) are blinks one but the laptop does not turn on.
I triedtoclean the connections, remove the batteries....no change.
Once i removed the RAM and the unit booted up.
So the issue is the following : it works with no RAM, but it does not work with installed RAM.
The problem is the same with the old and a brand new RAM also.
Any idea?