Thanks for the replies guys. After spending hours scraping the glue
off of about 1 tenth of the area, I've decided to just put down a
floating laminate floor. Most people think they look better, it costs
about the same, and in my situation it's a lot easier to install. It
recently rained for 25 days straight and there was no moisture at all
in my basement, so I think the laminate will be fine.

Tony.