...And, go into "Alt + p -> advanced -> programs" in Opera 12.17 and make sure it's set to check for defaults. Also, click "details" there and if it doesn't load "default programs" in windows and has a bunch of checkboxes for file types and protocols instead, make sure http and https are checked and click ok.
Switching on this morning still didn't solve the problem but Burnout's suggestion above did work without reinstalling everything.
Thank you very much!