This is among the three seriously bugging things which keep on bugging us users. The problem is usually the cookies which you have already deleted and that is certainly what I'd have advised you try first (important to do this in exact order and do it all):
1. Sign out of Google (having closed all but that one browser window- ie no other active windows/pages!),
2. Clear browser caches and cookies (since the beginning of time, not just the recent ones),
3. Disable ad-blockers (or any add-ons you might have installed for your browser which might be seen as circumventing YouTube policy),
4. Add YouTube and Google cookies (those with [*.]youtube.com and those with [*.]google.com) to your browser's third party exceptions, and-
5. restart (as in- close it and reopen it) your browser.
6. Sign in again.
7. "Rinse and repeat" (do over) if it didn't take or you didn't do it all the first time.
-but since you already HAVE and CAN at least sign in now- it is the other reason. This seems to concern the deletion of the YouTube channel but keeping its Google+ product. The fix would be to delete the Google+ product and essentially start over. BUT- if you are attached to the Google+ product then that wont be viable for you.