ExpressionEngine 2.5.2 site. I can login as me (super admin) and my client (non-super admin) on several browsers on my computer, and from iPad and iPhone via LTE, and my client could login on her old laptop. At the same location on her new laptop, she can't login. I stopped by and couldn't login as me or her on her computer, using IE9 or Chrome. Checked cookies, they are on, and working, but none get set on the Control Panel login page and it reloads the login page with no error. Caches cleared, cookies cleared, browser and computer restarted. I'm puzzled.
Chad, if you are in South Africa (SA?) then I strongly suspect you have an ISP (Telkom) / proxy related problem - something that has given me a few grey hairs in the past. Try setting "Require IP Address and User Agent for Login?" to off under Admin > Security and Sessions and set Control Panel Session Type and User Session Type to cookies only.