My blog network has the exact same problem. I have Jetpack Comments active on about a hundred blogs on my network. The "Post Comments" button is no longer active when using Google Chrome 22. I am using Jetpack 1.9.2 and WordPress 3.4.2.
I am able to post comments on the same site in Firefox 16 if I use the NoScript addon to block scripts from wp.com. As soon as I enable scripts from wp.com, the expand/collapse behavior of the comment box works again, and the "Post Comment" button is inactive just like it is in Chrome.
To complicate things further, the same comment form works perfectly in Safari 6.0.2.
Disconnecting the site's Jetpack from WordPress.com allowed the comments form to work in Google Chrome; however, the "Post Comments" button was still disabled in Firefox.
Https vs. http does not seem to be a factor. Both fail.
The first time this was reported by a user, I disconnected Jetpack from WordPress.com, then reconnected it. I was able to post comments again on that user's site. However, the user reported the same problem a few days later, and I confirmed the "Post Comments" button was again not active, so I just disabled Jetpack Comments on her site and went with the default WordPress comments. I would prefer not to have to do this on a hundred sites.
BTW, this is likely a completely different issue, but the expand feature of the comments box is seen as a clickjacking attempt by the Firefox NoScript addon. ("NoScript intercepted a mouse or keyboard interaction with a partially hidden element. Click on the image below to cycle between the obstructed and clear version.") I have to uncheck the "Keep this element locked (recommended) button" and OK to allow the comment form to expand.