ICloud on iPad isn't accepting my password, even though I know it's correct.

A screen keeps popping up every 10 seconds asking me to login to iCloud, then I enter my apple ID -- and I know my apple ID is correct because I've logged into it on 2 other devices -- but it's not being accepted. I'd be fine with just turning off / deleting iCloud from the iPad, but it says I need to login to iCloud to even do that, so I'm stuck with the popup screen every 10 seconds. I've noticed this question asked many many times here, and nobody seems to have given a solution yet. Please note that I'm not able to contact Apple customer service at the present time (unless they have a chat or email address available for my problem, which I've tried, and they don't), so please, if anybody just has a solution, I'd be very very appreciative.