The boardgame rules for railroad conversion state as follows:
• To use a captured enemy railroad (for
movement and supply), it is necessary to
“convert” it to the standard railroad of
one’s side (and repair any damage
suffered, real or imagined).
• An infantry unit must pass over the
railroad to be converted, using 1 extra
MP. Neither cavalry, nor artillery, nor an
HQ may convert it.
I gather two things from these provisions relating to the issues raised in this thread:
(1) To convert a railroad it must be "captured". Funny thing though, the rules do not appear to define "captured". Nor do the rules appear to define any form of hex "control". Such a concept, if it exists, must be a creation of the PC game alone. It's clear, though, that any sort of control that exists must equal "capture", and so the game should require that "area control" exist OR that no enemy units exist in that area in order to convert a railroad. That would reflect "capture".
(2) The PC game requirement that only a moving unit -- as opposed to a unit beginning its turn in an area -- may convert a railroad is a misinterpretation of the rules. "Passing over the railroad" is extremely vague, and certainly gives no temporal quality to the rule. The only seeming requirement is that an infantry unit is located "over" the railroad (in the same hex) and expend 1 MP to convert the rail
as a form of movement. So a unit should be able to begin a move in an area with an unconverted rail and immediately expend an MP to convert the railroad in its area. That would constitute "passing over" in the context of the rule.
Perhaps clicking the convert railroad symbol would simply deduct the requisite MP's from a unit's movement if an unconverted railroad exists in the area (if no eligible rail is present, the symbol/button would be nonfunctional).