1. 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. It sounds like there could be a problem with your ISP. Can you access any of these directly?
2. Are you using http:// or https:// see http://en.support.wordpress.com/https/
3.Which browser and version of it are you using?
4. Have you tried clearing your browser cache and cookies? http://www.google.com/support/accounts/bin/answer.py?hl=en&answer=32050
5. Is your browser version up to date? You can upgrade any browser version here. http://browsehappy.com/
6. Do you have third party cookies enabled?
8. Do you have another browser you can try?