It sounds like you may have two separate issues, but one of them definitely sounds like the starter. Once you get the starter sorted out, I would continue your process of elimination to figure out why it's dying once you get it started. I agree with some of the previous posters that it sounds like you may have a fuel issue of some sort.
Here's a writeup on the starter contact replacement:
http://www.toyota-4runner.org/3rd-gen-t4rs/63228-another-starter-contacts-removal-thread.html
Thank you SO MUCH for your input!
Just to clarify, the engine has never died after it's been started, so I can eliminate that anything with the fuel delivery system or fuel filter is an issue.
Based on this, it's most definitely the contacts. The write-up link you provided is super detailed too! I should be able to get under and take care of this myself.
Thanks! Thanks! Thanks!!!!
Will keep you guys posted as soon as I can get the new contacts and get under to replace.