Sounds more like the above cap is helping you, if anything. It's just in the wrong place, or doesn't have enough value.
Ugh, poorly designed products with EMC issues...
Presumably, when you touch the chassis or AC cord, you're adding just enough capacitance that it's shunting some RF energy away, reducing the voltage that's disturbing whatever is forcing the thing off and allowing it to start.
It's very roughly possible that some ferrite beads thrown over most cables will fix it (one or a few on the line cord, on the cable(s) connecting to the power supply inside, between other boards, etc.). Also possible they'll make things worse. Same goes with those blue (usually) caps -- they're usually placed between a common connection (a ground or minus, but not the safety ground as such) and a nearby shield, or to safety ground (as such). Examples are, mains to safety GND/shield; DC- to GND; DC- to output common/GND; output common to GND; between GNDs elsewhere in the circuit; etc.
Tim