On the surface, the old "404 Not Found" would be one problem - simply your computer saying "Hey! I can't access the other computer!". Those of us who work in computer and network troubleshooting know that there are dozens of possible causes for that one symptom.
We know, for a certainty, that if we persist in believing that there is one problem causing all of the "404 Not Found" errors, that one problem will never be solved. This symptom will be solved only with detail and determination, and lots of diagnostic work.
>> (Update: 5/18): Blogger Support is now suspecting a link between use of Google Apps, and the 404. If you are having this problem, please help us diagnose the problem. Describe your use of the following Blogger / Google applications / wizards, with any possible details (relevant dates would be useful), in setting up or maintaining your domain:
>> Forum thread links: bX-*00077
>> Copy this tag: bX-*00077