How do I remove the lines when using tables?

I have been trying to find a way to hide the lines when I use tables in this site: http://lpservicios.com/groups-affiliations. I have managed to do the site without using tables except for this page the link leads you too.

This is why I have been trying to do the site without using tables:

I have the width=”0″ and in my editor it is fine, but when I put it into WordPress…the lines stay.

I have tried to set the style=”padding: 6px 24px;” as this was recommended in another post, this did not help;

I have set the bodercolor=”white” as well, this does not help either.

As a test, I tried to set the width=”5″ just to see if this had an effect, and it did not so making changes in the table setting likely is not going to have an effect, so now I am lost.

This next item is likely related:

When I display the site in IE using tables, it is fine, except for the lines. In Chrome is is a bit messed up in terms of spacing, but tolerable. In Firefox, the page is really messed up for spacing, again, not to mention the lines.

Suggestions?