100M is the limit for 100baseT, so you're well within spec to just run Cat5 before the two places. (I'd run cat5e or cat6 to reduce the noise, though). I'm not sure what the limit for gigE is, but I've run it a little over 100M without much problems -- we just put a switch at each end as soon as it entered the buildings. If you can trench between the two points, this might be the easiest.
Call whatever utility companies to get the existing lines marked, rent a ditch digger (looks like a big chainsaw blade on a cart), glue some PVC conduit together (while running some pull line), and once it's all together, pull the copper and terminate it. If you don't have other obstructions in the way, it'll take a team of two a day to complete, and a few hundred dollars of supplies.
If that fails:
I can't remember the name of the guy, or the name of the site where he put up all of his information, but there was someone in Hawaii who had a lot of information about squeezing longer range out of wireless ethernet. I think he was using 802.11b, but it might've been 802.11a, this was before the term 'wifi' became popular, so I don't think it was 802.11g ... this would've been about the time when the pringles can trick was noticed (2001?2002?).
Hopefully, someone else can remember and provide a link. I want to say he was connecting public schools in Hawaii, and they had a school bus that would act as an access point for laptops and had a long-haul link back to the school.
... it's possible, as it was older, that he was using other wireless technology (wavelan?), which might be harder to get ahold of this year, or difficult to put to use.
update: it might've been ALOHAnet, but from what I can find while wrestling with free airport wifi trying to frame my screen screwing up everything, it was out of service by the time I was remembering it (and I could've sworn it was ethernet-based). It's possible that I'm remembering whatever was the followup to ALOHAnet.