Apple ID on El Capitan does not work at all

HI everyone,

so I had some issues installing El Capitan yesterday but after I put my MacBook Pro into safe mode it all worked out OK, besides the fact that El Capitan is making the 3 year old Mac run about as fast as a dying 5,000,000 year old tortoise but I will forgive that for now.

the main problem is, I cannot sign into my Apple ID in El Capitan *at all*. I have two step verification which worked fine in Yosemite. I would just create an app specific password for iMessage, FaceTime, etc. it worked the day of the installation before the actual installation. Now, however, when I try my regular password, it says "authentication error". When I try the app specific password, it says "wrong password". therefore, I can't sign into iMessage, FaceTime, iCloud, etc. and I cannot use AirDrop or Handoff BECAUSE I cannot sign in.

what do I do? Besides this, the rest of the system seems to work fine and I am sure that the ridiculously slow speed will subside after a few days.

also, please forgive my capitalization errors. I am typing on my iPad and this discussion forum doesn't capitalize normally for some reason.

thank you all for your help!