Strange - not read of this issue in years on this site.
Having all 4 windows roll down is not a standard runner function.
So I think the alarm (after manufacturer add on) may be involved here. Is yours the RS3200 or another model?
Do you have an FSM? It will contain the electrical circuit logic that can be used to debug (not the alarm's just the standard runner).
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2001 Limited 4WD - 346+K - SunfireRed\Thunder Cloud; - 265/75/16 Michelin A/T2s - Fat Pat's 1.5" BL - StopTech ANGLED rotors - In series 699 trans cooler, New Yota1 transmission, All new OEM suspension front to rear.