I'll second that bump. I've got a similar laptop to the OP, and I've got the exact same problem you all are having.
I've got a Toshiba l775d-s7340 with an AMD A6-3400M. I'm running LM 16 Petra with Cinnamon v2.0.14 and Linux Kernel 3.11.0-12-generic, and I've got seemingly random intermittent detection of the keyboard/trackpad, but without rhyme or reason to it.
I installed 16 as a release candidate a week before release and followed the upgrade insructions which seemed to go well. Advice from IRC recommended I do a fresh install of the official release, so I tried but when I booted into the Live USB Installer the keyboard and trackpad were not detected at all!
I have little knowledge of how to troubleshoot a problem like this but if/when I figure any of this out I'll post back as you're the first lot I've found online with this issue.
Also, I dual booting with crunchbang which has been my go-to distro for the past year and it's been almost 100% on this same laptop, but about 2% pf the time I get the same kayboard/trackpad issue that I have more frequently on Mint.
Now it's time to learn how these drivers are implemented and where to hunt for log errors.
Wish me luck!