side bars get messed up when changing themes

I have an issue when it comes to changing themes…I built my main wordpress site using a 3 column theme. In the left side bar, I have Adsense skyscraper 600×160 and below that in the same side bar I have a links section using the widget. In the right side bar I have a 1 page entry(static) and below I have my post entries and underneath is my category section.

Anyway , every time I try to change my theme using only 3 column themes to replace with, the links will usually show in both side bars and either the posts or categories will disappear or will show up under the wrong headings…..I have tried to edit the side bars to remove the links section from one side and place the posts and categories in the right places , but I am very new to php….it is certainly not as obvious as HTML !!

anyway any help or pointer in the right direction will be very much appreciated

heres a link to the site I am currently working on right now and I want to change the theme for a more attractive one without changing the side bar configurations
click here