I was able to get SQLite Ruby installed and working under cygwin using the following method.
1. Install the following cygwin packages,
Ruby > ruby (1.8.7-p358-2)
Database > sqlite3
Database > libsqlite3_0
Database > libsqlite3-devel
2. download the ruby gems src from,
save the tar file anywhere in the cygwin tree (I used /home)
3. unzip and unpack the tar,
gzip -d rubygems-1.8.24.tgz
tar xvf rubygems-1.8.24.tar
4. cd to /rubygems-1.8.24 and run,
ruby setup.rb install
5. update gems, (this didn't do anything for me)
gem update --system
6. install sqlite3-ruby with gems,
gem install sqlite3-ruby
This appeared to work, but I need to do some additional testing.
Now I need to get back to importing data from a text file. I will try to post something more in a day or so.