(1) How are connecting to the internet and to WordPress.com? The way you connect to the internet (mobile, satellite, DSL, dial-up) and to your blog, and how many proxy server jumps etc. it takes to connect can cause problems. There maybe be problems with your ISP and/or with the proxy servers. Also note that the main dashboard isn’t designed to work with touch devices through the tablet and smartphone browsers.
(2) Exactly which browser and version of it are you using. If you don’t know click here to find out > http://whatsmyuseragent.com/
If you are using IE9 in compatibility mode - disable that because it makes the browser render as if it's IE7 and IE7 is not supported.
If you are using any browser extensions and/or add-ons especially for "private browsing" disable them and see what happens.
(3) Have you tried using the secure https:// log-in?