My thoughts:
1) Try to appeal to them on a "right thing to do" level (if the same guy that sold the roof is with the new company, they should accept responsibility to some degree).
2) Appeal to their bottom line by ensuring they understand that they'll have a reference and a customer for life if they honor the warranty.
If they refuse to be cool...switch tactics:
3) Ensure they understand that they will be reviewed poorly on every business site that will accept your rating/explanation and that you will name the individuals that did the selling and the installation.
4) Let them know that you will be contacting every news/media organization with your story. Nobody wants "7 on Your Side running" an investigative report.
5) Bluff that you have a lawyer in the family that will handle your case on a complimentary basis.
In the end, the only thing you can do to get your money's worth is either appeal to their better nature or bolster or threaten their reputation. If none of that works, there's likely little recourse in terms of saving your dollars. Even with a "free" attorney, YOUR time would cost more than $750 and in the mean time you either leave the leaky roof or have it repaired by someone else.
Here's wishing you best of luck on them having a change of heart!
Best of luck!