Hi Vikas,
Sorry If I am spelling your name differently (just guessing that it may be you name).
After reading your problem, It looks to me that its a simple problem of level triggring. Means the chip/circuit in which this signal is transfering may be level capture circuit.
Let me explain in other way...
For every signal when ever its changing the stage from 0->1 or 1->0 then there are 3 stage where a circuit can trigger. Lever trigring (when there is no change in the state), rising edge trigring (when state changes from 0->1) and falling edge trigring (when state changes from 1->0).
Now in you case when power is on and then connect/disconect your probe , then System works properly because it is sensitive to the edge trigring. But when Power is OFF and you connect the Probe, System is not able to detect the rising edge, and that's the reason that when you are going to SWITCH the power , system doesn't start but when you disconnect the probe , it detect the falling edge and start working.
I think above explanation can help you to understand the problem.
Let me know if you need anyother help.