How much damage would be needed to allow for this war?

Say if the twin towers didn't fall or only the towers fell and there was no pentagon hit or PA happening or vice versa.

Do you think there would of been less chance of war if anything was different?

To be honest, no...
If the US government wanted a war, they'd get it anyway.
And if the WTC attack wasn't enough to get initial support then another attack could be arranged.
Besides, they went ahead without much public support in the first place, and they had very little foreign or UN support too.

No, if the government wanted a war, they'd get it whatever it took.