First, read "Concrete Abstractions" by Max Heilparin (http://gustavus.edu/+max/concrete-abstractions-pdfs/index.html) and "Simply Scheme" by Brian Harvey (http://www.cs.berkeley.edu/~bh/ss-toc2.html). Neither of these books assume much programming knowledge, and should be accessible to anyone.

Next, listen to or watch Brian Harvey's lectures for "The Structure and Interpretation of Computer Programs" (http://webcast.berkeley.edu/course_details.php?seriesid=1906978502). This course uses SICP as a text book, but takes a less mathematical approach. The lecture notes are also available (http://www-inst.eecs.berkeley.edu/~cs61a/reader/vol2.html). This is a full semester course, so it will take you a while to get through it, but Harvey's lectures are easy to listen to.

Third, watch the lectures by Holly Yanko (http://www.aduni.org/courses/sicp/index.php?view=cw) for a SICP course. These follow the book very closely, but Yanko covers the material at relaxed pace. Unfortunately, these videos are Real Player, so you may have difficulty playing them. There are notes for the first few lectures.

Finally, watch the videos of Abelson and Sussman (http://groups.csail.mit.edu/mac/classes/6.001/abelson-sussman-lectures/). At this point, you will certainly be able to understand the more subtle and/or complex points that they make.

Overall, this is a big commitment of time, but it will certainly shake you out of any rut that your current languages have put you in regarding how to solve problems with computers.