Yet another issue after rally cross (this one genuinely confusing)

So I ran today at the MLRC rally cross championship round 1, and all seemed well after we were done the final run. Nothing wrong with the car I could see or feel, the new winter tyres (unbalanced) did a great job. Then i switched back onto the road tyres (which i have had on the car for over a year) and everything went to hell in a handbasket. The car immediately started pulling left, HARD, which was a very new problem. First i thought it was the obvious stuff, could be a couple wheel weights fell off, or my pressures were way down, or i knocked it waaay out of alignment on the rough stage. I also thought perhaps i had bent or damaged some suspension component. But then i put the car in neutral... and it all went away... then i put it in first and started driving and everything started again only when it is in gear, even if its travelling the same speed in neutral it goes away. This has me somewhat flummoxed, as i can only think of one component which could possibly cause this, but if the diff was broken there would be horrible noises and it would have been pulling on the snow tyres as well... i cannot think of what is causing this, so i ask you guys... what the hell did i break?

What car do you have?

98 integra

I don't know this car's suspension in detail, but my guess would be; front suspension mounting point broken, loose or fastener missing, and that mounting point is loaded/opened-up by engaging the drivetrain.

It just might be hard to spot what's wrong when the vehicle is stationary.

we did a pretty thorough check of the car after the event, but i suppose its possible we missed something. I'll look into that, Thanks!

You may not have felt the pull on the snow tires if they were only used on snow/ice. Did you test the snow tires on the highway? Check for a broken engine mount or CV joint as well.

If an LSD, to test the diff, put the left wheels on dry tarmac, right on shoulder gravel and launch hard. Look for tire marks on the tarmac. Repeat with the other side.