Uploading a 24GB package via 'My Contents' will fail, as you cannot upload files this way larger than 10mb.
You are on the right track using the Share Package GP tool, and it might be worth trying from a different network location. (Home or External Office connection) You could also check with your IT Department to see if they are killing large request after XX amount of time, and ask them to monitor your upload.
If you continue to have issues uploading on a different network, please let us know.
Andrew