I like Gentoo, but it really wants a broadband internet connection.  If your install doesn't have that luxury, but you have access to a machine that does, here's a way to get the files you need to update with.  If you don't want the'world' of updates, work with the second form of the emerge command below.

Go to http://gentoo.osuosl.org/snapshots and get portage-latest.tar.bz2 (21mb at time of this writing - so yes, you likely need two trips to the internet connection)

tar xjf portage-latest.tar.bz2 from /usr, so it overwrites /usr/portage.  This will not delete files like 'emerge sync' does, so when you go to build you may find 'security violation' complaints about files in ebuild directories not in the manifest.  Note that, with a 33.6 connection a few hours after getting the portage-latest file, an 'emerge sync' took (only) 18 minutes including the time to update the portage cache.

emerge -puDv world or whatever target you like, fix any blockages reported and make note of any 'F' ebuilds which you will have to download manually.  Take note of the "Total size of downloads: " line at the end so you are prepared.  If you have a dialup connection and it says it will update portage, might as well do this now as it is not too big. 

emerge -puDf world 2>&1 > /dev/null | sed -e 's/ /\n/g' > toget.lst to generate the list of files to download

emerge -pf package 2>&1 > /dev/null | sed -e 's/ /\n/g' >> toget.lst to add any additional packages you'll want to install

put toget.lst on a portable storage device (usb hard drive, flash memory, whatever your plan is), and take it to your internet connection.  You may wish to add Heiko Herold's windows wget if you're stuck on the dark side.

wget -i toget.lst -nc -nd in the dir you want the files to appear should do it from there.  The options are : 
Finally, copy the downloaded files from your storage device to /usr/portage/distfiles and run the emerge -uD world or emerge package command as needed.