The quick reply box is at the bottom of the page, however, there is no quick reply button to click on in each person's replies in the thread so I can't use the quick reply box. Does that make sense?
All the way down at the bottom of the page, on the left-hand side, you should see a box that allows you to change "skins", i.e., the colors the pages are shown in. Try clicking through the various options to see if the "Quick Reply" button is visible.
I rather suspect that the latest vBulletin version isn't exclusively geared to IE, as more and more people are using alternative browsers like Firefox. Although I don't use Firefox as my default browser, I was using it today, and noticed some changes when viewing TCS.