1991 Accord won't start if out in rain

My cousin's Honda will turn over forever but not start when it's been parked out in the rain, or for a couple hours after raining.

She's taken it in and they've not been able to replicate the problem at the service shop, but they've replaced the distributor and the spark plugs and wires.

I thought it might be the infamous main relay problem (although it's not hot here, just wet), so I checked it and it clicks two seconds after turning the key. I pulled it out anyway and the solders don't look bad, but I re-did them anyway to be safe. Still no luck.

Any other ideas?