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How are you 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.
Have you tried resetting your router and modem, rebooting your computer
then logging in using the secure https:// log-in see http://en.support.wordpress.com/https/
Have you tried using another browser?
Exactly which browser and version of it are you using. If you don’t know click here to find out > http://whatsmyuseragent.com/