I have had the same issue, email archives that are complete from the mid-90s and sporadic emails from the 1980s. What I've been doing is archiving most of the messages in text files in mbox format , one file per month, and I gzip them after a certain period of time to conserve space.

Unfortunately 'grep' and similar utilities have been insufficient to do decent searches on them. What I ended up doing is building my own search utility in python. It allows me to specify multiple search terms, regular expressions or strings, search blocks of files (e.g. in this case finding blocks that are delimited by a starting '^From ' line), as well as automatically descending into directories, tar files, gzipped files, etc. With this I can easily run a search across any set of files that I desire (even if I've tarred and compressed them) and get out resulting output that I can read with a mail reader program such as Mutt. I've found it to be extremely useful for this, as well as almost all other search tasks that I do.

If you are interested in using it, I've made it available on github. It's at https://github.com/bruceisrael/search

Don't worry about browsers or any specific applications; just use iptables to not allow networking except to a small set of IP addresses that are whitelisted (the site to submit results, for example, and anything else you want to allow). Make sure that no sites that allow pass-throughs are on that list (e.g. no SSH servers).

This still doesn't prevent having a parallel machine with network access (a laptop, tablet, or smartphone), but kiosk mode wouldn't prevent that anyway.

FYI; In Thrice Upon A Time, http://www.amazon.com/Thrice-Upon-Time-James-Hogan/dp/0671319485, a scientist discovers the ability to sent particles back through time, affording the ability to send messages. At the same time, a giant fusion reactor starts to create mini-blackholes, and he needs to use this ability to send information back to correct things before disaster strikes. Published in 1980, it appears to predict and foreshadow much of the LHC issues, fears and discussions.
See http://en.wikipedia.org/wiki/Thrice_Upon_a_Time for more info.

Free as in speech, or free as in beer?

Here on slashdot there are lots of folks who are waiting with bated breath for you to tell them how to build a trap to catch real boobies.