Cant sign into iMac, but I can sign into iCloud.com and Apple.com

I went on a vacation for two weeks and came back last night. Today, I tried to sign into and it says "This account uses an iCloud password to log in. If you need to change the password use another device to change it at appleid.apple.com." I did this and changed my password, but it still wont let me log on; even though, I can log into iCloud.com and apple.com.

This computer was unboxed a little over a month ago. I can't tell you the specs or anything because I can't sign into it, and I don't remember. I'm also not sure which community to post this to and if it's in the wrong area or there is a better place, tell me, so I can repost it there please.

Any help would be greatly appreciated. Thank you.