Start up problem due to insufficient disk space

Often a safe boot will allow access to your storage:

http://support.apple.com/en-us/HT201262

If not then you can try Target Disk Mode connecting with another Mac.

http://support.apple.com/en-us/HT1661

Ciao.

If you are lucky Ogelthorpe's Safe Boot suggestion will allow you to get to the desktop - this works because during the Safe Boot process cache and log files are deleted/trimmed. Assuming you do get to the desktop, unless something was really awry with your system, your drive is still over full, its just that you now have the chance to remove some files to free up space. (1) if you use iPhoto launch it and delete iPhoto's trash can. This was something I hadn't thought of until one of the Level 6 or Level 7 folk mentioned it a while ago. Doing it freed up a significant amount of space on my MBA. (2) if you have a lot of music, videos, and digital photos those are good candidates for removing from your internal hard drive. Deleting one movie or a few CDs will probably free up more space than deleting all your documents and a couple programs.

I purchased a low profile SD cardfor my MBA and moved all my media to it which freed up a tremendous amount of space.