Join Date: Jul 2007
Location: San Francisco/Sydney
Programs: UA 1K/MM, Hilton Diamond, Marriott Something, IHG Gold, Hertz PC, Avis PC
Posts: 8,156
You can definitely make a claim against United, and will likely have no real issues getting that one paid.
For Turkish, you can technically covered by both EU261 AND the equivalent Turkish government legislation which is very similar to EU261.
EU261 covers the delay to your final destination, so through your initial flight out of the EU may have only been delayed a few hours, the number that counts is the total delay (~24 hours). The Turkish government rules would cover for the same delay, although obviously you aren't going to be able to double-dip from TK over that.
Getting compensation out of TK likely won't be easy and they are known for being difficult about it - but technically you are due compensation so it should be possible to win in the end...
(Standard EU261/etc exceptions apply, and I'm presuming none of the delays were caused by "extraordinary circumstances" as defined by the EU/Turkish government)