Sounds like impedance bleed or static buildup from the hill wiring, to me. The external monitor is introducing an extra drain path. The start wiring is the longest antenna, since the start is the longest wire path and therefore is most vulnerable to noise.
Try this:
1) Disconnect the hill wiring, and any scoreboards, from the timer and the PC (leave the timer attached to the PC, with both turned on).
2) Plug the monitor into the PC.
If this doesn't cause false starts and you're not using an optocoupler, then you've found the problem. Get an opto. Everybody timing ski races should be using an opto anyway. You can buy a TAG Heuer HL553 opto from Ted Savage at Precision Timing in Montreal.
http://www.precisiontiming.com