I just wanted to mention another possible issue regarding the failure of ancestry.com to work on FF.
I followed the instructions above, and I still could not get ancestry to work in FF. Ancestry DID work in IE, but I prefer not to use IE. BTW, I am running FF 19.0.2 on Win 8.
So, I started looking at my Add-ons and Plugins. To access Add-ons go to Tools-->Add-ons. Click on Add-ons, and you will be taken to your FF Add-ons page, so you can see what you have.
I disabled all of them and ancestry worked fine on FF. Then I added each one back to see which one(s) were the problem, For me, it was Ghostery 2.9.3 that was the issue. So, now I disable it whenever I go on ancestry,com.
So, it may be the same Add-on (ghostery), or another Add-on that is giving you the problem, rather than a cache or cookie problem.