Notwithstanding the fact that I have given you the code that will do what you want and without wishing to offend you are suffering from a number of common misconceptions which I will try and explain more clearly and may help with your decision.
The first is that there is not just one size of viewport ( the area in which your page is displayed in a browser) as that depends on the resolution the user has set, the size of the device they are using and whether they have their browser open fully or not (few people open their browsers fully anyway). So what you see on your computer is not what I see on my computer especially as I have many windows open and the browsers tucked into half the screen
When you open a sidebar in the browser (such as the history or favourites panel) then all you are doing is reducing the space available for your display. Its the same as grabbing the edge of the browsers and making the browser smaller as far as your content is concerned.
If you have designed your page at a fixed width (which you have) then nothing can change that fixed width without re-coding the elements in the page to adjust accordingly. The only reasonable solution for your sidebar (without re-coding the whole thing) is to implement the code I gave you. This will put the sidebar on the right but maintain a min-width. When you open your history panel the content will get pushed to the right and the right sidebar will disappear off the right of the viewport and the browser will show a horizontal scrollbar so that you can scroll to it. This is what the code I gave you will do in all the major browsers (except ie9 and under unless you change the doctype).
Not changing the doctype is simply not an option as you can’t use something from last century and expect it to function on modern browsers. If you don’t change it then you can’t use min-width as that was only available since ie7 and as I have already said you are forcing ie9 and under to render like IE5 and not understand much css at all.
Without using min-width I can’t see an easy fix. You culd possibly float the sidebar to the right and then the content to the left but this would mean that your sidebar would move to the top of the page when you narrow the screen and look abit odd with all your content dropping below it. Alternatively move your sidebar html after the closing div of your Content wrapper and then float the content to the left (width the exact width) and the float the sidebar to the right. When the screen is narrowed the sidebar will dropdown under the content and not obscure it. I believe these are the only suitable options for you at the moment.
As an aside you keep mentioning IE8 as though it is the main browser but its usage is down to 7% and chrome is the major contender now at 44% with Firefox at 20% and ie9+ at 15%. Ie8 is a marginal browser and in a couple of years will be gone.
However, and I can’t stress this enough, if you don’t change your doctype then ie9 and under will render like IE5 and use the broken box model, contain millions of bugs, need haslayout everywhere, not understand min or max-width, the child selector, hover on anything except anchors…the list goes on.
I really urge you to reconsider and jump into the 21st century. Lavish some tender loving care to that page as it is a bit of a mish mash of outdated design techniques and frankly looks broken even though that’s how you wanted it to look. This is meant as constructive criticism as we have all been in the same boat at some time
BTW you also have some scripts running that are crashing my browser as I have lost this post three times now:( (which could be because of one of the 136errors)