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.
But check your cache, too.