The problem is not the weeds, it's that the lawn is not healthy. A healthy lawn will crowd out the weeds. You've already found out that chemicals don't really work to fix the problem and actually make it worse in the long run.
Here's some general things that work to have the best lawn in the neighborhood:
Aerate the soil with a core aerator. The soil is likely to be compacted and that prevents air and nutrients from getting to the grass roots.
Take samples and get the soil tested so you know what the deficiencies are.
Water in a thin layer of compost into the newly aerated lawn (no it doesn't smell)
Quit using the Wal-mart fertilizer and get some good organic stuff. Actually Scott's markets a line of organics now. The results of the soil test will guide you on what you need. A high nitrogen fertilizer is like crack for the grass; it goes like crazy for a while then collapses. You want to build a good, deep root structure that will support a dense lawn that keeps the weeds from growing. Deep roots also require less watering.
It took me two seasons to get my lawn's issues mostly corrected from the previous owner's misdeeds. For the past 10, I've to do nothing but fertilize it in the spring and fall and it looks great. I mow it on the high side, leave the clippings there, and water when it needs it. That's all.
