Here are some easy steps to fix the missing button.
Step 1: Go to the three dots on the right of Chrome and go down to settings.
Step 2: Click on ABOUT on the left side in grey, then let good update or if it is up to date move to step 3. After it updates it should ask you to relaunch, relaunch it.
Step 3: Click on SETTINGS in grey on the left and go scroll all the way down until you see SHOW ADVANCED SETTINGS... in blue and click it.
Step 4: Locate PRIVACY and click the 2nd button under it CLEAR BROWSING DATA...
Step 5: This will open a new window, in this windows make sure the drop down menu is set to the beginning of time. Also the only boxes you need check are cookies and cache. Compare yours to this image. Then click CLEAR BROWSING DATA.
Step 6: Select EXTENSIONS in grey on the top left. Scroll down until you see Proctorio and click the trash can on the right of it and choose remove.
Final Step: Now close Chrome completely. Reopen Chrome and attempt to join the exam again. It should prompt you to install proctorio. Follow the instructions and reinstall then your Take quiz now button should reappear.