Try installing Zotero into a new Firefox profile and see if it starts up there. If that works, we can help you transfer your Firefox and Zotero data to the new profile.
I'd also recommend scanning your system for malware, if you're not already. (Not sure if that McAfee scanner in your screenshot is up to date.) It's possible that could be causing this, though not sure exactly how.
Can you try creating a fresh Firefox profile and then installing Zotero again? You can delete the test profile later, or keep it if it fixes the issue.
ReferenceError: dw_locktimer is not defined js.php:1:771748
TypeError: $tree.dw_tree is not a function js.php:1:360173
TypeError: History.getState is not a function _zoterowwwAll.bugly.1411506646.js:4478:20
Use of getPreventDefault() is deprecated. Use defaultPrevented instead. js.php:1:0
Is that immediately after starting up? There's no Zotero error in there, so what error exactly are you getting? Is this from the Ctrl+Shift+J browser console?
Sorry, running out of ideas here. Since Zotero Standalone is working, what Zotero Standalone version do you have?
I'd also recommend scanning your system for malware, if you're not already. (Not sure if that McAfee scanner in your screenshot is up to date.) It's possible that could be causing this, though not sure exactly how.
If you haven't, you can try uninstalling Firefox completely and then reinstalling it. I'm not sure there's any reason that would be any different from a regular reinstall, but it's one more thing to try.
I'd also recommend scanning your system for malware, if you're not already. (Not sure if that McAfee scanner in your screenshot is up to date.) It's possible that could be causing this, though not sure exactly how.
ReferenceError: dw_locktimer is not defined js.php:1:771748
TypeError: $tree.dw_tree is not a function js.php:1:360173
TypeError: History.getState is not a function _zoterowwwAll.bugly.1411506646.js:4478:20
Use of getPreventDefault() is deprecated. Use defaultPrevented instead. js.php:1:0
Sorry, running out of ideas here. Since Zotero Standalone is working, what Zotero Standalone version do you have?