Upon the knowledge that CD/vBulletin isn't detecting the browser properly, perhaps the easiest solution would be to install a User Agent switcher, which changes the information sent to webservers so that it appears that you're using a different browser than you are.
Here's one for Chrome. Installing it adds a button next to the address bar. Click it and select one of the other browser choices. Any of the Firefox options brought back the Quick Links and other features when I tried them. In the same menu, you can click Settings and then add an entry in the Permanent Spoof List for chiefdelphi.com to make it only send the false data to CD and not to other sites.
EDIT: For anyone who's paranoid about installing extensions, this functionality is apparently already built into Chrome: press Control-Shift-I (or F12, or Menu>>Tools>>Developer Tools) to open the Developer Tools, click the gear in the bottom-right corner, click Overrides, then check the User Agent checkbox and pick one of the options.
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FRC 2046, 2007-2008, Student member
FRC 1708, 2009-2012, College mentor; 2013-2014, Mentor
FRC 766, 2015-, Mentor