Repeater powers the rail but cart is not starting [duplicate]
Solution 1:
The basic principle of starting minecarts with Powered Rails is that the minecart needs to "know which way to go". By this, I mean there must only be one possible way for the minecart to move.
A sloped Powered Rail works because the minecart knows to move downhill. Another way to do this without sloping the rail is to put a solid block on one side of the Powered Rail. By doing this, the minecart should start moving the other way when the rail is powered.