I tried this in BU's quick cost estimator: 2 parent 1 child household, $100k income, $1 million house with no mortgage, $100k in savings.
Results: $44700 need-based scholarship, $29400 parent/student contribution, $3500 student loan, $2000 student work-study.
Going back and changing it to not have a house changes the need-based scholarship to $54600 and drops the parent/student contribution to $19500, leaving the rest unchanged.
Restoring the million dollar house but taking away the $100k savings makes the scholarship $49600 and the parent/student contribution $24500.
Finally, getting rid of both house and savings, leaving just the $100k income makes the scholarship $59500 and the parent/student contribution $14600.
So...it looks like having $100k in savings adds about $5000 to your expected contribution, and having a $1 million mortgage free house adds about $10k to your expected contribution.
I also tried it with $100k in a retirement account, and that changed nothing. $100k in non-retirement account investments was the same as $100k in savings.
It looks like you are going to have to have a lot more in income and/or non-retirement assets to actually get anywhere near full sticker price.