Since November 2013, Youtube received a forced integration with Google+, something no one saw coming, something no one “appreciates”. Anyway, since then, a Google+ account is required to comment on a Youtube video. Fortunately, it’s not required anymore :)
Then why can’t you comment on Youtube? The source of this problem would be the “Cookies” on your internet browser. Youtube and Google+ are 2 different websites. Google+ is considered “third-party” to Youtube while Youtube sees Google+ as “third-party”. If your internet browser has the function to “Block third-party cookies” enabled, or if accepting third party “cookies” is disabled, then we will need to change that. Just make an “Exception” for both the two sites on your browser and it’s good to go. Do not entirely disable the “cookies third party” blocker, however, it will put your computer in security risk, from viruses and all.
If the problem persists, your account itself could have been compromised. It is now posting spam to random Youtube videos, usually offering a fake site that promises fortune but is just a scam to get your money. The account has been blocked, and you probably wouldn’t be able to log-in again if you ever log-out. In that case, try contacting Google to help clear your account. Just don’t hold a high hope that you are getting it back, just make a new one, it’s not like anyone is using Google+ for other reasons anyway.