Thank you for your replies. I tried these plugins and other similar ones but they don’t solve the problem.
I noticed that when placing the same widget into the header custom widget area, it works on IE8, so maybe the problem is in the footer.php file.
I noticed some lines of code in the header.php file that say:
<!–[if IE 8]>
<style>
So, I thought that maybe I should add some code in my footer.php file but the thing is I have no idea what to put. Any ideas would be appreciated.